Question

Find component of A=2i+3j along B=3i+4j

Answer 1

A = 2i + 3j
B = 3i + 4j

|A| = √(2² + 3²) = √(13)
|B| = √(3² + 4²) = 5

A · B = |A||B| cosθ
|A| cosθ = [ A · B ] / |B|
= [ 6 + 12 ] / 5
= 18 / 5
= 3.6

Component of A along B is 3.6

Answer 2

The correct answer is 3.6.

Given: A = 2i + 3j

B = 3i + 4j

To Find: Component of A along B.

Solution:

Firstly, calculate the magnitude of A and B.

|A| = $\sqrt{2^{2} +3^{2} } =\sqrt{13}$

|B| = $\sqrt{(3^{2} + 4^{2} )}$ = 5

A · B = |A||B| cosθ

Component of A along B.

|A| cosθ = $\frac{[A.B]}{|B|}$

= $\frac{[6+12]}{5}$

= $\frac{18}{5}$

= 3.6

Hence, component of A along B is 3.6.

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