Question

find the scalar product of A = i + j and B = j​

Answer 1

Given:

$1) \: \vec{A} = \hat{i} + \hat{j}$

$2) \: \vec{B} = \hat{j}$

To find:

• Scalar product between the vectors?

Calculation:

Scalar product (also known as DOT product) can be defined as :

• When two vectors a and b at an angle $\theta$ is provided, the scalar product of the two vectors is given as a.b = ab$\cos(\theta)$.

• In a vector form, it can be calculated as :

$\vec{A}. \vec{B} = ( \hat{i} + \hat{j}).( \hat{j})$

$\implies \vec{A}. \vec{B} =(1 \times 0) + (1\times 1)$

$\implies \vec{A}. \vec{B} =0+1$

$\implies \vec{A}. \vec{B} =1$

So, the value of scalar product is 1 .

Answer 2

Explanation:

A

.

B

=(

i

^

+

j

^

).(

j

^

)

\implies \vec{A}. \vec{B} =(1 \times 0) + (1\times 1)⟹

A

.

B

=(1×0)+(1×1)

\implies \vec{A}. \vec{B} =0+1⟹

A

.

B

=0+1

\implies \vec{A}. \vec{B} =1⟹

A

.

B

=1

So, the value of scalar product is 1 .