Question

find the component of vector a =3i+4j along the direction of b =2i - 3j

Answer 1

Hi dear...here is your answer....

Answer 2

Explanation:

It is given that,

Vector, $a=3\overrightarrow{i}+4\overrightarrow{j}$

Vector, $b=2\overrightarrow{i}-3\overrightarrow{j}$

We have to find the component of vector a along the direction of vector b.

$N=\overrightarrow{a}.\hat{b}$

$N=\overrightarrow{a}\dfrac{\overrightarrow{b}}{|b|}$.............(1)

$|b|=\sqrt{2^2+(-3)^2}=3.6$

$N=(3i+4j).\dfrac{2i-3j}{3.6}$

$N=-1.6$

So, the component of vector a =3 i+4 j along the direction of b =2 i - 3 j is -1.6.

Hence, this is the required solution.