Question

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

Answer 1

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

$\theta = 65.56°$