Chapter 9: Q. 58 (page 628)

Show that if u and v are orthogonal then
$||u \times v|| = ||u|| ||v||$

Short Answer

Expert verified

To show $||u \times v|| = ||u|| ||v||$ , first write for any two vectors and substitute the value of $θ$ in the given equation and solve.

Step by step solution

Step 1. Given information.

Consider the given question,

$||u \times v|| = ||u|| ||v||$

For any two vectors $||u \times v|| = ||u|| ||v|| \sin θ$

If uand v are orthogonal then $θ = 90 ° u ⊥ v$ , that is to say $θ = 90 °$ .

Step 2. Substitute the value of θ in the given equation.

Substitute the value of $θ$ in the given equation,

$||u \times v|| = ||u|| ||v|| \sin θ ||u \times v|| = ||u|| ||v|| \sin 90 ° ||u \times v|| = ||u|| ||v|| \cdot 1 ||u \times v|| = ||u|| ||v||$

Therefore, $L H S = R H S$ .

Hence, $||u \times v|| = ||u|| ||v||$ proved.

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Show that if u and v are orthogonal then
$||u \times v|| = ||u|| ||v||$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the value of θ in the given equation.

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Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the value of θ in the given equation.

One App. One Place for Learning.

Most popular questions from this chapter

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Show that if u and v are orthogonal then
$||u \times v|| = ||u|| ||v||$