Compute the scalar projection of u onto v where u = (4, 2, 0) and v = (-1, 2, 1).

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $25.99Unlock all

Get ready for your Honors Mathematics 3 exam with our engaging quizzes. Use flashcards and multiple choice questions with explanations to enhance your study. Prepare effectively for the test!

Multiple Choice

Compute the scalar projection of u onto v where u = (4, 2, 0) and v = (-1, 2, 1).

Explanation:
The scalar projection of u onto v is the component of u in the direction of v, found by (u·v)/||v||. Compute the dot product: 4(-1) + 2(2) + 0(1) = -4 + 8 + 0 = 4? Wait, that’s wrong. Let’s correct: 4(-1) + 2(2) + 0(1) = -4 + 4 + 0 = 0. Since the dot product is zero, u has no component in the direction of v, so the projection length is 0. The magnitude of v is sqrt((-1)^2 + 2^2 + 1^2) = sqrt(6), but 0 divided by any nonzero number is 0. Geometrically, u is perpendicular to v, so its shadow along v has length 0. Therefore, the scalar projection is 0.

The scalar projection of u onto v is the component of u in the direction of v, found by (u·v)/||v||. Compute the dot product: 4(-1) + 2(2) + 0(1) = -4 + 8 + 0 = 4? Wait, that’s wrong. Let’s correct: 4(-1) + 2(2) + 0(1) = -4 + 4 + 0 = 0. Since the dot product is zero, u has no component in the direction of v, so the projection length is 0. The magnitude of v is sqrt((-1)^2 + 2^2 + 1^2) = sqrt(6), but 0 divided by any nonzero number is 0. Geometrically, u is perpendicular to v, so its shadow along v has length 0. Therefore, the scalar projection is 0.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy