Calculus 3 Test 1

calculate. (-5,9)-(8,-3)

(-13,12)

calculate linear combinations 1/2(4,-2,10)-1/3(12,3,3)

(-2,-2,4)

calculate the cross product assuming that u×v=(2,5,0) v×(u+v)

(-2,-5,0)

let v=(6,7,3) which of the following vectors points in the same direction as v? (6,-7,-3) (12,14,6) (3,7,6) (-7,-3,6)

(12,14,6)

find the length to the following vectors: (a) 3i+4j (b) 6i-5j (c) i+j (d) i-5j

(a) 5 (b) √61 (c) √2 (d) √26

compute the dot product (8j+8k) . (i-6k)

-48

calculate the cross product (k+i) × j

-i+k

calculate the cross product. (4i-5j+6k) × (i+j-9k)

39i+42j+9k

If P=(-7,4) and Q= (1,6), find the coordinates of the vector PQ→

PQ→= (8,2)

Find the components of PQ→ P=(5,-1), Q=(9,2)

PQ→=(4,3)

What is the Terminal point Q of the vector a=(1,5) based at P=(6,2)?

Q=(x,y)=(7,7)

calculate the cross product assuming that u × v = (6,5,8) v × u

(-6,-5,-8)

let v=(6,7,3) which of the following vectors is parallel to v? (-7,-3,6) (6,-7,-3) (-6,-7,-3) (3,7,6)

(-6,-7,-3)

Let v=PQ→, where P=(2,1) and Q= (8,-6). Which of the vectors with the following given tails and heads are equivalent to V? (-3,3),(7,10) (0,0),(10,-7) (-1,2),(9,-5) (4,-5),(-6,-12)

(0,0),(10,-7) (-1,2),(9,-5)

find the point of intersection of the lines r(t)=(1,0,0)+t(-3,3,0) and s(t)=(0,1,1)+t(0,0,3)

(0,1,0)

find a vector parametrization r(t) for the line with the given description. passes through (1,1,1) and (6,-5,3)

(1+5t,1-6t,1+2t)

calculate. (5,3)+(9,2)

(14,5)

find the given vector. esubv, where v=(2,5,2)

(2/√33,5/√33,2/√33)

find a vector parametrization for the line passing through P=(3,9,8) with direction vector v=(3,-2,-4). (use t for the paramterized variable.)

(3+3t, 9-2t, 8-4t)

find a vector that is orthogonal to (-3,6,6)

(4,1,1)

calculate. 5(8,6)

(40,30)

find a vector parametrization for the line passing through the origin and the point P=(4,-4,-2). (use t for the paramterized variable.)

(4t,-4t,-2t)

calculate v × w v=(4,3,5), w=(3,1,4)

(7,-1,-5)

find the given vector. unit vector e making an angle of 3π/7 with the x-axis.

(cos(3π/7),sin(3/7))

find a vector parametrization for the line with the given description. perpendicular to the yz-plane, passes through (0,0,4)

(t,0,4)

find v . e where ‖v‖=5, e is a unit vector, and the angle between e and v is 2π/3. v . e

-5/2

calculate the linear combinations 7(4j+2k)-3(2i+7k)

-6i+28j-7k

compute the dot product j . i

0

find the cosine of the angle between the vectors (0,1,4),(2,0,0)

0

let v=i+j+k, and w=7i+8j-5k. compute the dot product. v . w

10

assume that u . v=2, ‖u‖=1, and ‖v‖=3. Evaluate the expression. 7u . (4u-v)

14

compute the dot product. (7,10,10) . (1,0,1)

17

determine whether the two vectors are orthogonal and if not, whether the angle between them is acute or obtuse. (-5,0,-2), (-4,-5,1) orthogonal, acute, or obtuse?

acute

let v=i+6j and w=8j+11k. Find the cosine of the angle θ between v and w.

cos(θ) = 48√5/185

determine whether AB→ is equivalent to PQ→ A=(1,1,1) B=(3,3,3) P=(7,6,4) Q=(9,8,6)

equivalent

determine whether the vectors AB→ and PQ→ are equivalent. A=(15,8), B=(6,8), P=(6,8), Q=(-3,8)

equivalent

determine whether vectors AB→ and PQ→ are equivalent. A=(3,1), B=(7,4), P=(4,-5), Q= (8,-2)

equivalent

find the given vector. unit vector esubv where v=(9,40)

esubv=(9/41,40/41)

determine whether the vectors AB→ and PQ→ are parallel, and if so, determine whether they point in the same direction. A=(1,1), B=(3,4), P=(1,1), Q=(11,16)

parallel in the same direction

Determine whether or not the two vectors are parallel. u=(-4,1,6), v=(8,-2,12)

the vectors are not parallel

let R= (-18,12). calculate the following. the components of u=PR→, where P=(19,16).

u=(-37,-4)

find the vector v=PQ→ P=(1,0,1), Q=(1,4,6)

v=(0,4,5)

find the components and length of the vector v=9i+8j-7k

v=(9,8,-7) ‖v‖=√194

find the given vector. vector w of length 2 in the direction opposite to v=i-j

w=(-√2,√2)

let v=P₀Q₀→, where P₀=(1,-4,3) and Q₀=(0,1,-5). Is the following vector (with tail P and head Q) equivalent to v? P=(1,2,4), Q=(0,7,-4)

yes

find all scalars λ such that λ(2,6) has length 1.

±1/√40

find the angle between v and w if v . w=‖v‖‖w‖.

θ=0

find the angle betwen the vectors. use a calculator if necessary. (5,1,-1) and (1,-3,2)

θ=π/2

let R=(5,3). Calculate the length of OR→.

‖OR‖=√34

find the length of the vector v=(4,3,9)

‖v‖= √106