Vectors Question 216

Question: Component of the vector $ \vec{A}=,2\hat{i}+3\hat{j} $ along the vector $ \vec{B},=(\hat{i}+,\hat{j}), $ is

Options:

A) $ \frac{5}{\sqrt{2}} $

B) $ 4\sqrt{2} $

C) $ \frac{\sqrt{2}}{3} $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Component of $ \vec{A} $ along $ \vec{B}=,A,\cos ,\theta =,\frac{\vec{A}.\vec{B}}{B} $

$ =\frac{2+3}{\sqrt{1+1}},=\frac{5}{\sqrt{2}} $