Dot & Cross Products

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Multivariable Calculus › Dot & Cross Products

Questions 1 - 2

1

Let , and .

Find $u\times v$ .

$u\times v=(10,-30,20)$

$u\times v=(10,30,20)$

$u\times v=(40,-20,12)$

$u\times v=(-10,30,-20)$

$u\times v=(0,-3,2)$

Explanation

We are trying to find the cross product between and .

Recall the formula for cross product.

If , and , then

$u\times v=(u_yv_z-u_zv_y, -u_xv_z+u_zv_x, u_xv_y-u_yv_x)$ .

Now apply this to our situation.

$u\times v=(4(10)-5(6),-2(10)+5(-2), 2(6)-4(-2))$

$u\times v=(40-30,-20-10, 12+8)$

$u\times v=(10,-30,20)$

2

Let , and .

Find $u\times v$ .

$u\times v=(10,-30,20)$

$u\times v=(10,30,20)$

$u\times v=(40,-20,12)$

$u\times v=(-10,30,-20)$

$u\times v=(0,-3,2)$

Explanation

We are trying to find the cross product between and .

Recall the formula for cross product.

If , and , then

$u\times v=(u_yv_z-u_zv_y, -u_xv_z+u_zv_x, u_xv_y-u_yv_x)$ .

Now apply this to our situation.

$u\times v=(4(10)-5(6),-2(10)+5(-2), 2(6)-4(-2))$

$u\times v=(40-30,-20-10, 12+8)$

$u\times v=(10,-30,20)$

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