Projection of u onto v and v onto u Given the vector u = <−2,6,



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Projection of u onto v and v onto u
Given the vector u=<2,6,4> and a vector v such that the vector projection of u onto v is <2,4,4>, and the vector projection of v onto u is <8,24,16>. What is the vector v?
Let v=<a,b,c>
Projection of v on u is given by:
On comparing u.v224=1
Dividing both sides by 2 we get:

Answer & Explanation



Beginner2021-12-15Added 33 answers

The projection of u onto v is a scalar times v. So from the given information we have v=λ(2,4,4).
Hence projuv=vuuuu=λ914(2,6,4).
It is given that this projection is (8,24,16),so λ=569 and hence
Karen Robbins

Karen Robbins

Beginner2021-12-16Added 49 answers

Here is a more tangent way to solve this problem:
Notice v and the projection of u onto v must have the same direction, therefore we can assume v=λ(2,4,4),
in which λ is a constant to be determined. Now use the other condition to establish the equation
Solve this to get λ=569. Therefore, v=569(2,4,4).

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