Let the vectors x = (-0.3, –4.6, –3) and y = (4.1, –-2.2, r) Determine the value of r such that the two vectors are orthogonal. Your answer should be the value of r as a decimal number with three digits to the right of the decimal point.

Let →a=⟨−2,0,5⟩ and →b=⟨−3,−2,4⟩.Find the angle between the vectors (in degrees).

Determine the vector 8a – 7b if a = -3i + 2j – 4k and b = 5i + 6j + 2k. 8a – 7b = help (vectors)

Find the vector expression for the line that is the intersection of the planes 3x−3y−2z=−2 and −4x+2y+z=−4. Use t as the parameter in your vector expression.

Graph the vector 3 – 2i and state its argument (or direction vector) in degrees.

1. Let x = i +4j + 2k and y = i-3j - k. In this question, write all vectors in i, j, k notation. (a) ( Find |x||. (b) M Find 2x + 3y. (c) Find x. y. (d) Find x × y. Answer: Answer: Answer:

use vectors

Given the same three points P (1, 4, 6), Q (-2, 5, -1)  and R (1,  -1, 1).  Find a vector equation of the line segment from Q to R.

Find the vectors T, N, and B at the given point. = (²2², ²²3³, c), (₁, - ²/₁, -1) -3, T = N = B = r(t)

a. Write the vector (8, 5, 30) as a linear combination of a₁ = (4, -4,1), d₂ = (4, -5, 5) and d3 = (0, -4,-4). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ +52 + 6ả3, which would be entered as 4a1 + 5a2 + 6a3. (8,5, 30) = b. Represent the vector (8,5,30) in terms of the ordered basis B = {(4,-4, 1), (4, −5, 5), (0, -4,-4)}. Your answer should be a vector of the general form . [(8, 5, 30)] B =