Question

V
Find the angle between v=i+2j+3k and w=4i-k.
:2
.

Answer 1

86.28 degrees

Explanation:

Angle between vectors is

`\cos(x) = (cross \: product)/(magnitudes \: multiplied)`

The cross product is

`4 + 0 - 3 = 1`

The magnitudes of first vector is

`\sqrt{1 {}^(2) + 2 {}^(2) + 3 {}^(2) } = √(14)`

The second vector magnitude is

`√(17)`

So the magnitudes multiplied is

`√(14) * √(17) = √(238)`

So our equation will be

`\cos(x) = (1)/( √(238) )`

`x = \cos {}^( - 1) ( (1)/( √(238) ) )`

X is about 86.28 degrees