# Vectors Questions and Answers

Math

VectorsDescribe the transformations to the parent function. Check all boxes that apply.
y = -(x - 5)² +3
Reflects across the x-axis (opens down)
shifts right 5
shifts left 5
shifts up 5
shifts down 5
shifts right 3
shifts left 3
shifts up 3
shifts down 3

Math

VectorsFind the angle 0 (in radians) between the vectors. (Round your answer to two decimal places.)
u = 6i + 8j
v = -2j

Math

VectorsFind the projection of u onto v.
u = (4,8)
v = (6,-3)
Write u as the sum of two orthogonal vectors, one of which is projvu

Math

VectorsLet B =
be any 2 x 2 matrix.
and a such that
(i) Show that there are real numbers
as a scalar multiple of a unit vector, and hence find an
expression for u in terms of a and c.

Math

VectorsDetermine whether u and v are equivalent. Explain.
Vector Initial Point Terminal Point
Interpret your results.
u and v have the same magnitude and direction so they are equivalent.
u and v have the same magnitude but not the same direction so they are not equivalent.
u and v have the same direction but not the same magnitude so they are not equivalent.
u and v do not have the same magnitude or direction so they are not equivalent.

Math

VectorsGiven the following vector v:
v = (-2,-4)
Step 2 of 2: Find the linear combination of i and i that is equivalent to v.

Math

VectorsGiven the following vector v:
Step 1 of 2: Find a unit vector pointing in the same direction as v.
v = (-2,-4)

Math

VectorsFind the magnitude and direction angle (in degrees) of the following vector.
Answer 5 Points
v = 5(cos(37°)i + sin(37")j)
Recall that answers entered in degrees will require a degree symbol, which is located in the keypad.
|||v|| =
0=

Math

VectorsFind the magnitude and direction angle of the following vector. Write your angle in degrees rounded to four decimal places.
u = 3i + 7j

Math

VectorsConsider the function f(x,y) = x² - 2x²y+3y² +5 and the point P(-1,3).
a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P.
b. Find a vector that points in a direction of no change in the function at P.
a. What is the unit vector in the direction of steepest ascent at P?
<_,_>
(Type exact answers, using radicals as needed.)
What is the unit vector in the direction of steepest descent at P?
<_,_>(Type exact answers, using radicals as needed.)
b. Which of the following vectors is in a direction of no change of the function at P?
A. (8,-16)
B. (-16,8)
C. (-8,16)
D. (-16,-8)

Math

VectorsA football was thrown into the air at a speed of 37 miles per hour at an angle of 50 from the horizontal. Express this velocity in vector form. Round your answer to four decimals.

Math

VectorsDetermine the value of k such that the planes 2x-3y+kz=4 and ky-z+3=0 are perpendicular and the value of k such that the planes are parallel.
k = 2, no such value
k = 0, no such value
no such value, k = 0
no such value, k = 2

Math

VectorsThe area of the parallelogram whose adjacent sides are given by the vectors
a = 3i + j + 4k and b = i - j +k
(A) √50
(B) √42
(C) √44
(D) None of these

Math

VectorsFind the point that is symmetric to the point (0, -3) with respect to the x-axis, the y-axis, and the origin
The point symmetric to (0, -3) with respect to the x-axis is
(Type an ordered pair.)
The point symmetric to (0, -3) with respect to the y-axis is
(Type an ordered pair.)
The point symmetric to (0, -3) with respect to the origin is
(Type an ordered pair.)

Math

VectorsLet u and u be two vectors in an inner product space so that ||u||= 6, |v||=2 and the angle between the two vectors is 30°. Find the angle between vector u+3v and vector u-4v

Math

VectorsThe vector PQ has initial point P(1, -3) and terminal point Q(4, -6). Find the magnitude and direction of PQ.
Select the correct answer below:
|PQ|=6√2; θ=315°
|PQ|=3√/2 θ = 225°
|PQ|-6√2; θ= 135°
|PQ|=3√2; θ= 135°
|PQ|=3√2; θ=315°
|PQ|=6√2; θ = 225°