11th Grade Physics: Chapter 4
True/False: Vector addition is the same as scalar addition.
False
True/False: Vector subtraction is commutative.
False (ex. vector 2 - vector 3 = vector -1 but vector 3 - vector 2 = 1)
True/False: Coordinate systems are not important when solving problems with vectors as long as the proper scalars are used.
False, coordinate systems are key when determining vector problems.
True/False: cos = opposite/hypotenuse
False, cos = adjacent/ hypotenuse
True/False: Two vectors are considered equal as long as they have the same magnitude.
False, equal vectors must have the same direction and magnitude.
True/False: Mathematical techniques in vector operations are subject to drawing errors.
False, geometric techniques are.
True/False: Scalar multiplication of a vector has no effect on its orientation.
False, if the scalar is negative, it can reflect the vector across the coordinate plane.
True/False: When adding vectors graphically, it is not necessary to draw them to scale.
False, if you don't draw a vector to scale, you are more likely to misinterpret the component values.
True/False: The ratios of the lengths of corresponding sides in similar triangles are rarely the same.
False, in corresponding triangles, the ratios will always be the same.
True/False: The sum of the angles in any triangle is equal to 360°.
False, it is equal to 180°.
True/False: In vector operations, geometric techniques are more accurate than mathematical equations.
False, mathematical equations will always be more accurate.
True/False: Reference angles are never negative.
False, reference angles can be negative.
True/False: Vector reference angles are always positive acute angles.
False, reference angles can be negative.
True/False: For two vectors, *M* and *N*, |*M* + *N*| = |*M*| + |*N*|.
False, substitute M and N with the numbers -2 and 3 and you will see that the answers are different.
True/False: tan = adjacent/opposite
False, tan = opposite/adjacent
True/False: The perpendicular components of a two-dimensional vector and the magnitude of the vector itself may be negative.
False, the magnitude of a vector is always positive.
True/False: The congruence of sides of triangles determines similarity.
False, the proportional ratios of sides determines triangle similarity.
True/False: The sum of one vector of 5 units and another of 1 unit, represented as sides of a right triangle, is 6 units.
False, the resultant is the square root of 26 (square root of (5^2 + 1^2) )
True/False: Scalar vector components are always positive.
False, they can be negative.
True/False: Vectors can be used only in two dimensions.
False, though we only use 2D vectors in this chapter, more than two dimensions can exist for a vector.
True/False: The vector angle of a vector is always a positive acute angle.
False, vector angles can be obtuse.
How could vectors be used to help predict the motion of hurricanes?
Motion vectors are placed at the eye of the storm and every few hours a new photo of the atmospheric motion vectors (AMV) was taken to track the storm's motion.
How is the direction of a vector affected when it is multiplied by a scalar?
The direction stays the same if the scalar is positive, but a negative scalar points the vector in the opposite direction, as full 180° reflection across the coordinate plane.
True/False: 3(T+P) = 3T + 3P
True
True/False: A position vector's tail is always placed at the origin of the frame of reference.
True
True/False: For two vectors, *M* and *N*, |*M* - *N*| = |*N* -*M*|.
True
True/False: If the vector's reference angle is 32° and its vector angle is 148°, the vector is in the second quadrant.
True
True/False: In order to analyze a vector, identifying a coordinate system is essential.
True
True/False: The Pythagorean theorem may be used to determine the magnitude of the resultant if the X and Y vector components, representing the sides of a right triangle, are known.
True
True/False: The reference angle and vector angle may be the same value for a given vector.
True
True/False: The scalar components of a two-dimensional vector may both be negative, but the scalar magnitude of the vector is always positive.
True
True/False: The vector resultant of an object's changes in position is the same as its displacement.
True
True/False: To find the unknown acute angles in a right triangle when you are given only the lengths of the sides, use the corresponding inverse trigonometric operations.
True
True/False: Two vectors that are added together to produce a resultant are called the components of the resultant.
True
True/False: Vectors can be multiplied by scalars.
True
True/False: Vectors can be subtracted from other vectors.
True
True/False: When a vector is multiplied by a scalar, the direction of the vector remains the same unless the scalar is a negative number.
True
True/False: When illustrating vectors, the indicator of the magnitude of the vector is the orientation of the arrow.
True
True/False: When resolving a vector into its components, it is helpful to draw an accurate sketch.
True
True/False: sin = opposite/hypotenuse
True
If a vector's reference angle is 50° and the vector angle is 50°, which quadrant does the vector lie in? a. I b. II c. III d. IV
a
The resultant is the arithmetic sum of the magnitudes only if a. the vectors are in the same direction b. the vectors are in opposite directions c. one vector is perpendicular d. the magnitudes of the vectors are the same
a
Which is another way to write 0°? a. 090T b. 000T c. 45° north of west d. 425° e. North
a
Which of the following is not an essential part of a vector diagram? a. vector head b. vector component c. vector tail d. vector tip
a
right triangle
a triangle containing a 90° angle
The symbol for the angle used to determine the scalar components of a vector is _______.
alpha
If a vector's reference angle is 40° and the vector angle is 140°, which quadrant does the vector lie in? a. I b. II c. III d. IV
b
When resolving vectors into components or finding resultants, _______ is/are more accurate than ________. a. geometric techniques; mathematical techniques b. mathematical techniques; geometric techniques c. geometric vector addition; geometric vector subtraction d. mathematiacal vector addition; mathematical vector subtraction
b
Which of the following dimensions belongs in the set {force, velocity, acceleration, magnetic field}? a. speed b. displacement c. temperature d. mass
b
Which of the following is a vector? a. mass b. *F* c. F d. temperature
b
Which of the following may you do to a vector without changing it? a. Rotate a vector through any angle other than 360 degrees b. Move the vector without changing its orientation c. Multiply a vector by a scalar other than 1 d. Add a nonzero vector to a vector
b
If a vector's reference angle is 10° and the vector angle is 190°, which quadrant does the vector lie in? a. I b. II c. III d. IV
c
If a vector's reference angle is 45° and it lies in the third quadrant, what is the vector angle? a. 45° b. 135° c. 225° d. 315°
c
If you know the length of both legs of a right triangle, which operation would be the correct one to find the acute angles? a. tan absolute value (a) b. tan absolute value (a/b) c. tan^-1 absolute value (a/b) d. tan^-1 absolute value (a)
c
Which is not necessarily true about similar triangles? a. Their corresponding sides are proportional b. Their angles are sufficient to determine similarity c. Their corresponding sides are congruent d. Their corresponding angles are congruent
c
Which of the following is always positive? a. vector b. scalar c. magnitude d. direction
c
Which of the following map directions is equivalent to the Cartesian 180°? a. 000T b. 090T c. 270T d. 360T
c
The projections of a vector into its coordinate axes are the _____________ of the vector.
components
The projections of a vector onto its coordinate axes are the ____________ of the vector.
components
If a vector's reference angle is 50° and the vector angle is 310°, which quadrant does the vector lie in? a. I b. II c. III d. IV
d
What does the commutative property of vectors say? a. Vectors can be transported b. Vectors can be inverted c. Vectors can be subtracted in any order d. Vectors can be added in any order
d
Which is not true about a vector's magnitude? a. It cannot be negative b. It cannot be greater than the sum of the magnitudes of its components c. It is a scalar quantity d. Trigonometry is necessary to compute it from component vectors
d
Which is true about similar triangles? a. All angles are acute angles b. Angles are not involved in determining similarity c. Corresponding angles are not congruent d. Corresponding sides are proportional e. Sides are congruent
d
When multiplying a vector by a positive scalar number, the vector's _________ stays the same.
direction
sine (theta)
in a right triangle, the ratio of the length of the side opposite to the acute angle theta to the length of the hypotenuse
When illustrating vectors, the indicator of the magnitude of the vector is the ________ of the arrow.
length
Two vectors are considered equal if they have the same _____________.
magnitude and direction
component vectors
one of two or three vectors that are parallel to the designated coordinate axes that are summed to produce the resultant vector
Triangles containing a 90° angle are called _______ triangles.
right
Two vectors that are added together to produce a resultant are called ____ of the resultant.
sum
A vector diagram has three essential parts: the tip, the magnitude, and the _____.
tail
reference angle
the acute angle between a vector and its horizontal component vector
When illustrating vectors, the indicator of the direction of the vector is the ____ of the arrow.
tip
similar triangles
triangles with congruent corresponding angles
Map directions are measured from _________.
true North (geographic North)
You can compute all unknown parts of a right triangle if you know the measures of any _______ parts.
two
