Question

If u and v are orthogonal to w, then u·v is orthogonal to w.

A) True
B) False

Answer 1

False. The dot product of vectors u and v is not necessarily orthogonal to vector w.

Step-by-step explanation:

False

If u and v are orthogonal to w, it means that u and v are perpendicular to w. In other words, the angle between u and w is 90 degrees, and the angle between v and w is also 90 degrees.

To determine whether u·v is orthogonal to w, we can calculate the dot product of u·v and w. If the dot product is zero, then u·v is orthogonal to w. However, if the dot product is nonzero, then u·v is not orthogonal to w.