Vectors Questions and Answers

Describe 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

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

Find 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

Let 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.

Determine 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.

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

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

Find 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=

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

Consider 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)

A 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.

Determine 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

The 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

Find 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.)

Let 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

The 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°