What is the vector projection of vector u = (4, 2) onto vector v = (3, 0)?
Answer and explanation
Correct answer: D. (4, 0)
- Step 1: Formula: proj_v(u) = ((u . v) / |v|^2) v. Dot product u . v = 43 + 20 = 12. Step 2. |v|^2 = 3^2 + 0^2 = 9. proj_v(u) = (12 / 9) (3, 0) = (4/3) (3, 0) = (4, 0). Answer: (4, 0). Why not the others:* The projection extracts the component of u in the direction of v.
Practise more Conic Sections, Vectors, Mathematical Proof and Sequences.
Free questions with an explanation for every one, and full timed New Zealand Scholarship mock tests.
More Conic Sections, Vectors, Mathematical Proof and Sequences questions
- What are the coordinates of the foci of the ellipse x^2 / 25 + y^2 / 16 = 1?
- What are the equations of the asymptotes of the hyperbola x^2 / 9 - y^2 / 16 = 1?
- What is the scalar (dot) product of vectors u = 3i - 4j and v = 2i + 5j, and what is their angular relationship?
- What is the sum to infinity of the geometric series 12 + 4 + 4/3 + 4/9 + ...?
- In mathematical proof by induction, what are the two required procedural steps?
- Prove that sqrt(2) is irrational by contradiction. What initial assumption is made and where does the contradiction arise?