Question

Given the magnitude of two vectors |⃗| = 4 and |⃗⃗| = 6, and |⃗ + ⃗⃗| = 8. Find the angle between the vectors ⃗ and ⃗⃗(when they are placed tail to tail). = ∠(⃗, ⃗⃗)

Answer 1

Answer:

the angle between the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$  is  $cos\phi = \frac{1}{6}$

Step-by-step explanation:

Given -

$|\overrightarrow{a}| = 4$ , $|\overrightarrow{b}| = 6$ ,  $|\overrightarrow{a} + \overrightarrow{b} | = 8$

If two vector $\overrightarrow{a}$ and $\overrightarrow{b}$ are inclined at an angle $\phi$

vector parallelogram method

$|\overrightarrow{a} + \overrightarrow{b} |^{2} = |\overrightarrow{a}|^{2} + |\overrightarrow{b}|^{2} + 2 |\overrightarrow{a}||\overrightarrow{b}|cos\phi$

64 = 16 + 36 + 48 $cos\phi$

$cos\phi = \frac{1}{6}$