Question

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

Answer 1

Answer:

86.28 degrees

Step-by-step explanation:

Angle between vectors is

$\cos(x) = \frac{cross \: product}{magnitudes \: multiplied}$

The cross product is

$4 + 0 - 3 = 1$

The magnitudes of first vector is

$\sqrt{1 {}^{2} + 2 {}^{2} + 3 {}^{2} } = \sqrt{14}$

The second vector magnitude is

$\sqrt{17}$

So the magnitudes multiplied is

$\sqrt{14} \times \sqrt{17} = \sqrt{238}$

So our equation will be

$\cos(x) = \frac{1}{ \sqrt{238} }$

$x = \cos {}^{ - 1} ( \frac{1}{ \sqrt{238} } )$

X is about 86.28 degrees