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marishachu [46]
3 years ago
9

Please i need your help to solve this question. I will give the brainliest.

Mathematics
1 answer:
Maksim231197 [3]3 years ago
8 0

Step-by-step explanation:

The angle between vectors is given by

\cos{\theta} = \dfrac{\vec{\textbf{a}}\cdot \vec{\textbf{b}}}{|\vec{\textbf{a}}||\vec{\textbf{b}}|}

The magnitudes for the vectors are as follows:

|\vec{\textbf{a}}| = \sqrt{a_x^2 + a_y^2 + a_z^2}

\:\:\:\:\:\:\:=\sqrt{(2)^2 +(-5)^2 + (3)^2} = 6.16

|\vec{\textbf{b}}| = \sqrt{b_x^2 + b_y^2 + b_z^2}

\:\:\:\:\:\:\:= \sqrt{(3)^2 + (1)^2 + (4)^2} = 5.10

The dot product between the vectors is

\vec{\textbf{a}}\cdot \vec{\textbf{b}} = (2)(3) + (-5)(1) + (3)(4) = 13

Therefore, the angle between the two vectors is

\cos{\theta} = \dfrac{\vec{\textbf{a}}\cdot \vec{\textbf{b}}}{|\vec{\textbf{a}}||\vec{\textbf{b}}|} = \dfrac{13}{(6.16)(5.10)}

or

\theta = 65.56°

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