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denis23 [38]
3 years ago
15

Find the angle between the vectors ????=????+???? and ????=−????+????. (Give an exact answer. Use symbolic notation and fraction

s where needed.)
Mathematics
1 answer:
joja [24]3 years ago
7 0

Answer:

The angle between them is 60 degrees

Step-by-step explanation:

Given

a = 2i + j -3k

b = 3i - 2j -k

Required

The angle between them

The cosine of the angle between them is:

\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}

First, calculate a.b

a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)

Multiply the coefficients of like terms

a \cdot b =2 * 3 - 1 * 2 - 3 * -1

a \cdot b =7

Next, calculate |a| and |b|

|a| = \sqrt{2^2 + 1^2 + (-3)^2

|a| = \sqrt{14

|b| = \sqrt{3^2 + (-2)^2 + (-1)^2}

|b| = \sqrt{14}

Recall that:

\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}

This gives:

\cos(\theta) = \frac{7}{\sqrt{14} * \sqrt{14}}

\cos(\theta) = \frac{7}{14}

\cos(\theta) = 0.5

Take arccos of both sides

\theta =\cos^{-1}(0.5)

\theta =60^o

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