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Chapter 10: Q. 19 (page 824)

If u and v are vectors in 鈩�3 such that u路v=0 and u脳v=0, what can we conclude about u and v?

Short Answer

Expert verified

u路v=0andu脳v=0 concluded that at least one of them is0.

Step by step solution

01

Step 1. Given Information 

If u and v are vectors in 鈩�3 such that u路v=0 and u脳v=0, what can we conclude about u andv?

02

Step 2. If u and v are vectors in ℝ3 such that u·v=0 and u×v=0.

u路v=0 if vectors u and v are orthogonal.

The cross product u脳v=0 is u and v are parallel.

Now we can also say that u路v=0andu脳v=0concluded that at least one of them is 0.

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