The scalar product of two vectors vecA =2 hati+2 hatj- hatk and vecB = - hatj+ hatk, is given by

Question

The scalar product of two vectors vecA =2 hati+2 hatj- hatk and vecB = - hatj+ hatk, is given by (A)  vecA. vecB = 3  (B)  vecA . vecB = 4  (C)  vecA . vecB = -4  (D)  vecA . vecB = -3

Tardigrade Admin · Accepted Answer

Given, A=2 hati+2 hatj- hatk and B=- hatj+ hatk Scalar product A ⋅ B=(2 hati+2 hatj- hatk) ⋅(- hatj+ hatk) Using hati ⋅ hati=1, hatj ⋅ hatj=1, hatk ⋅ hatk=1=1 we have A ⋅ B=-2-1=-3

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

$A . B = 3$

$A . B = 4$

$A . B = - 4$

$A . B = - 3$

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 $A \cdot B = - 2 - 1 = - 3$

Q. The scalar product of two vectors A=2i^+2j^​−k^ and B=−j^​+k^, is given by

A.B=3

A.B=4

A.B=−4

A.B=−3