PHYSICS-Chapter 4
True
A is a correct symbol for a vector. True False
True
A position vector's tail is always placed at the origin of the frame of reference.
True
A resultant vector extends from the tail of the first vector to the head of the second. True False
True
A scalar has only magnitude. True False
False
A vector has only magnitude. True False
True
Adding the opposite of vector B to vector A is the same as subtracting vector B from vector A. True False
True
All similar triangles have proportional sides. True False
False
Cartesian angles have "T" after the numerical value. True False
True
Cartesian angles start from the positive x-axis. True False
False
Equal vectors have opposite directions. True False
vector's reference angle = 67°
If a vector is in the first quadrant and its vector angle is 67°, what is the vector's reference angle? vector's reference angle = -23° vector's reference angle = 23° vector's reference angle = 67° vector's reference angle = 113° vector's reference angle = 157°
III
If a vector's reference angle is 10° and the vector angle is 190°, which quadrant does the vector lie in? I II III IV
III
If a vector's reference angle is 10°and the vector angle is 190°, which quadrant does the vector lie in? I II III IV
II
If a vector's reference angle is 40° and the vector angle is 140°, which quadrant does the vector lie in? I II III IV
θ = 225°
If a vector's reference angle is 45° and it lies in the third quadrant, what is the vector angle? θ = 45° θ = 135° θ = 225° θ = 315°
tan−1 |a/b|
If you know the length of both legs of a right triangle, which operation would be the correct one to find the acute angles? tan |a| tan |a/b| tan−1 |a/b| tan−1 |a|
False
In vector operations, geometric techniques are more accurate than mathematical techniques. True False
True
Map directions have "T" after the numerical value. True False
False
Map directions start from the positive x-axis. True False
True
Some scalars, such as temperature, can be negative. True False
True
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 False
the tail of A to the tail of B.
The difference of vectors A and B can be constructed by placing the tip of A to the tip of B. the tip of A to the tail of B. the tail of A to the tip of B. the tail of A to the tail of B.
True
The magnitude of a vector is always positive. True False
False
The ratios of the lengths of corresponding sides in similar triangles are rarely the same. True False
the vectors are in the same direction.
The resultant is the arithmetic sum of the magnitudes only if the vectors are in the same direction. the vectors are in opposite directions. one vector is perpendicular to the other. the magnitudes of the vectors are the same.
True
The scalar components of a two-dimensional vector may both be negative, but the scalar magnitude of the vector is always positive. True False
True
The sum of the angles in any triangle is equal to 180°. True False
False
The sum of the angles in any triangle is equal to 360°. True False
True
The vector resultant of an object's changes in position is the same as its displacement. True False
True
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 False
right
Triangles containing a 90° angle are called __________ triangles.
magnitude and direction.
Two vectors are considered equal if they have the same magnitude. direction. magnitude and direction. Vectors can never be equal.
True
Two vectors that are added together to produce a resultant are called the components of the resultant. True Fasle
True
Vector addition is commutative. True False
False
Vector addition is the same as scalar addition. True False
True
Vector reference angles are always positive acute angles. True False
False
Vector subtraction is commutative. True False
True
Vector subtraction is not commutative. True False
True
Vectors are equal if they have both the same magnitude and the same direction True False
True
Vectors can be multiplied by scalars. True False
True
Vectors can be subtracted from other vectors. True False
Vectors can be added in any order.
What does the commutative property of vectors say? Vectors can be transported from one location to another. Vectors can be inverted. Vectors can be subtracted in any order. Vectors can be added in any order.
its magnitude changes, but its direction stays the same.
When a vector is multiplied by a positive scalar number, its magnitude changes, but its direction stays the same. its direction changes, but its magnitude stays the same. both its magnitude and its direction change. both its magnitude and its direction stay the same.
True
When a vector is multiplied by a scalar, the direction of the vector remains the same unless the scalar is a negative number. True False
True
When adding vectors graphically, it is necessary to draw both of them using the same scale. True False
True
When adding vectors graphically, it is not necessary to draw both of them using the same scale. True False
length
When illustrating vectors, the indicator of the magnitude of the vector is the ____________ of the arrow.
direction
When multiplying a vector by a positive scalar number, the vector's ________________ stays the same.
True
When resolving a vector into its components, it is helpful to draw an accurate sketch. True False
mathematical techniques; geometric techniques
When resolving vectors into components or finding resultants, ______ is/are more accurate than ________. geometric techniques; mathematical techniques mathematical techniques; geometric techniques geometric vector addition; geometric vector subtraction mathematical vector addition; mathematical vector subtraction
True
When the directions of the vectors are not identical, the resultant is not equal to the sum of the magnitudes of the two legs. True False
090T
Which is another way to write 0°? 090T 000T 45° north of west 425° North
Trigonometry is necessary to compute it from component vectors.
Which is not true about a vector's magnitude? It cannot be negative. It cannot be greater than the sum of the magnitudes of its component vectors. It is a scalar quantity. Trigonometry is necessary to compute it from component vectors.
displacement
Which of the following dimensions belongs in the set {force, velocity, acceleration, magnetic field}? speed displacement temperature mass
F - bold
Which of the following is a vector? mass F - bold F - capital italicized temperature
270T
Which of the following map directions is equivalent to the Cartesian 180°? 000T 090T 270T 360T
180T
Which of the following map directions is equivalent to the Cartesian 270°? 000T 090T 135T 180T 270T
Move the vector without changing its orientation.
Which of the following may you do to a vector without changing it? Rotate the vector through any angle other than 360 degrees. Move the vector without changing its orientation. Multiply the vector by a scalar other than 1. Add a nonzero vector to the vector.
Move the vector without changing its orientation.
Which of the following may you do to a vector without changing it? Rotate the vector through any angle other than 360°. Move the vector without changing its orientation. Multiply the vector by a scalar other than 1. Add a nonzero vector to the vector.
right triangle
a triangle containing a 90° angle right triangle reference angle component vectors similar triangles
component vectors
one of two or three vectors that are parallel to the designated coordinate axes that are summed to produce the resultant vector right triangle reference angle component vectors similar triangles
reference angle
the acute angle between a vector and its horizontal component vector right triangle reference angle component vectors similar triangles
similar triangles
triangles with congruent corresponding angles right triangle reference angle component vectors similar triangles