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

the angle between the vectors
`\overrightarrow{a}` and
`\overrightarrow{b}` is
`cos\phi = (1)/(6)`

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 = (1)/(6)`