Question

Let y=[[ 4; -9; -1 ]] and u=[[ 3; -6; -6 ]]. Write y as the sum of two orthogonal vector

Answer 1

To write y as the sum of two orthogonal vectors, we can find the projection of y onto a vector and subtract it from y.

Step-by-step explanation:

To write y as the sum of two orthogonal vectors, we can find the projection of y onto a vector and subtract it from y. Let's take u as a vector orthogonal to y. To find u, we can use the cross product between y and another vector. In this case, let's take the cross product between y and the vector [1, 0, 0].

Using the cross product formula, we have u = y x [1, 0, 0] = [(-9)(0) - (-1)(-6), (-1)(1) - (4)(0), (4)(0) - (-9)(1)] = [6, -1, 9].

Therefore, y can be written as the sum of the vectors [6, -1, 9] and [-6, -9, -8].