Question

The scalar product of two vectors $ \vec{A} =2\hat{i}+2\hat{j}-\hat{k} $ and $\vec{B} = -\hat{j}+\hat{k}, $ is given by

• A. $ \vec{A}. \vec{B} = 3 $
• B. $ \vec{A} .\vec{B} = 4 $
• C. $ \vec{A} . \vec{B} = -4 $
• D. $ \vec{A} . \vec{B} = -3$

Answer 1

The Correct Option is D

Given, $A=2 \hat{i}+2 \hat{j}-\hat{k}$ and $B=-\hat{j}+\hat{k}$
Scalar product $A \cdot B=(2 \hat{i}+2 \hat{j}-\hat{k}) \cdot(-\hat{j}+\hat{k})$
Using $\hat{i} \cdot \hat{i}=1, \hat{j} \cdot \hat{j}=1, \hat{k} \cdot \hat{k}=1=1$
we have $A \cdot B=-2-1=-3$