Question

Suppose u = (-1, 3, 0) and v = (-5, -1, -4). Then: 1. The projection of u along v is <-5/2, -1/2, -4/2>. 2. The projection of u orthogonal to v is <-16/21, 64/21, 4/21>. Results for this submission # Entered Input Preview Message 1 <-2.5,-0.5,-2> (-5/2, -1/2, -4/2) The first coordinate is incorrect The second coordinate is incorrect The third coordinate is incorrect 2 <-0.761905,3.04762,0.190476> (-16/21, 64/21, 4/21) At least one of the answers above is NOT correct.

          Suppose u = (-1, 3, 0) and v = (-5, -1, -4). Then:
1. The projection of u along v is <-5/2, -1/2, -4/2>.
2. The projection of u orthogonal to v is <-16/21, 64/21, 4/21>.
Results for this submission
# Entered Input Preview Message
1 <-2.5,-0.5,-2> (-5/2, -1/2, -4/2) The first coordinate is incorrect The second coordinate is incorrect The third coordinate is incorrect
2 <-0.761905,3.04762,0.190476> (-16/21, 64/21, 4/21)
At least one of the answers above is NOT correct.

Suppose u = (-1, 3, 0) and v = (-5, -1, -4). Then:
1. The projection of u along v is <-5/2, -1/2, -4/2>.
2. The projection of u orthogonal to v is <-16/21, 64/21, 4/21>.
Results for this submission
# Entered Input Preview Message
1 <-2.5,-0.5,-2> (-5/2, -1/2, -4/2) The first coordinate is incorrect The second coordinate is incorrect The third coordinate is incorrect
2 <-0.761905,3.04762,0.190476> (-16/21, 64/21, 4/21)
At least one of the answers above is NOT correct.

Added by Tina M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/31/2023

Step 1

To do this, we use the formula: proj_v(u) = (u • v / ||v||^2) * v where "•" denotes the dot product and "|| ||" denotes the magnitude. u • v = (-1)(5) + (3)(-1) + (0)(2) = -5 - 3 = -8 ||v||^2 = (5)^2 + (-1)^2 + (2)^2 = 25 + 1 + 4 = 30 So, proj_v(u) = (-8/30) * Show more…

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Suppose u = (-1, 3, 0) and v = (-5, -1, -4). Then: 1. The projection of u along v is <-5/2, -1/2, -4/2>. 2. The projection of u orthogonal to v is <-16/21, 64/21, 4/21>. Results for this submission # Entered Input Preview Message 1 <-2.5,-0.5,-2> (-5/2, -1/2, -4/2) The first coordinate is incorrect The second coordinate is incorrect The third coordinate is incorrect 2 <-0.761905,3.04762,0.190476> (-16/21, 64/21, 4/21) At least one of the answers above is NOT correct.