First slide

Vectors

Question

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

Moderate

A

A· B = 3
B

A· B = 4
C

A· B = $-$ 4
D

A· B = $-$ 3

Solution

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 $\hat{i} \cdot \hat{i} = 1, \hat{j} \cdot \hat{j} = 1, \hat{k} \cdot \hat{k} = 1$
We have, $A \cdot B = - 2 - 1 = - 3$

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