Chapter 9: Q. 63 (page 628)

If $u \cdot v = 0$ and $u \times v = 0$ , what, if anything, can you conclude about $u$ and $v$ .

Short Answer

Expert verified

We can conclude that at least one of the vectors $u, v = 0$ or have an angle of $90^{0}, 0^{0}$ between them.

Step by step solution

Step 1. Dot product

We know,

$u \cdot v = |u| |v| \cos θ$

For $u \cdot v = 0$ ,

Either $|u| = 0 |v| = 0 \cos θ = 0 \Rightarrow θ = 90^{0}$

Step 2. Cross Product

We know,

$u \times v = |u| |v| \sin θ$

As given,

For $u \times v = 0 \Rightarrow |u| = 0 o r \Rightarrow |v| = 0 o r \Rightarrow \sin θ = 0 o r θ = 90^{0}$

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If $u \cdot v = 0$ and $u \times v = 0$ , what, if anything, can you conclude about $u$ and $v$ .

Short Answer

Step by step solution

Step 1. Dot product

Step 2. Cross Product

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If u·v=0and u×v=0, what, if anything, can you conclude about u and v.

Short Answer

Step by step solution

Step 1. Dot product

Step 2. Cross Product

One App. One Place for Learning.

Most popular questions from this chapter

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If $u \cdot v = 0$ and $u \times v = 0$ , what, if anything, can you conclude about $u$ and $v$ .