Question

Find the angle between A and B vector

A = 4i^ and B = ( -3i^ +3j^)


I need step .


answer => 135°

Answer 1

!! Hey Mate !!

your answer is --

Given, vector A = 4i^ and B = (-3i^+3i^)

now,

Magnitude of A is

$\sqrt{ {4}^{2} } = 4$

and magnitude of B is

$\sqrt{ {( - 3)}^{2} + {3}^{2} } \\ \\ = \sqrt{9 + 9} = \sqrt{18} \\ \\ = 3 \sqrt{2}$

Now, A + B = 4i^ - 3i^ + 3j^ = i^ + 3j^

magnitude of A+B is

|A+B| =
$\sqrt{ {1}^{2} + {3}^{2} } = \sqrt{10}$
Let,angle between them is @

Also, magnitude of A+B is

|A+B| = √A^2+B^2+2ABcos@

=> √10 = √4^2+(3√2)^2+2×4×3√2cos@

=> 10 = 16+18+24√2cos@

=> 10 = 34+24√2cos@

=> 10-34 = 24√2cos@

=> √2cos@ = -24/24

=> cos@ = -1/√2

=> cos@ = -√2/2

=> cos @ = cos 135°

[ cos135° = -√2/2]

=> @ = 135°

Hence,angle between two vectors is 135°

【 HOPE IT HELPS YOU】

Answer 2

hope it will help you