Question

9. Find b so that the vectors v=5i +2j and w=4i+b are orthogonal.

Answer 1

b = -10

Explanation:

Two vectors are orthogonal if and only if their dot product is zero. The dot product of v and w is given by:

(v · w) = (5i + 2j) · (4i + bj) = 5 * 4 + 2 * b = 20 + 2b.

For v and w to be orthogonal, we need the dot product to be zero, which means 20 + 2b = 0, so:

2b = -20

b = -10

Therefore, b = -10 makes the vectors v and w orthogonal.