Question

Find the scalar product of the vectors.
i +2 j +3 k, 2 i -5 j +k​

Answer 1

Answer:

- 5

Step-by-step explanation:

To Find :-

Scalar product of the vectors :-

$\hat{i}+ 2\hat{j}+ 3\hat{k} \: and \: 2\hat{i}- 5\hat{j}+ \hat{k}$

Solution :-

Scalar product of the vectors :-

$\hat{i}+ 2\hat{j}+ 3\hat{k} \: and \: 2\hat{i}- 5\hat{j}+ \hat{k}$

$= (\hat{i}+ 2\hat{j}+ 3\hat{k}) \times (2\hat{i}- 5\hat{j}+ \hat{k})$

$= \hat{i}(2\hat{i}) + 2\hat{j}(-5\hat{j}) + 3\hat{k}(\hat{k})$

= 1(2) - 2(5) + 3(1)

= 2 - 10 + 3

= 2 + 3 - 10

= 5 - 10

= - 5

Hence, Scalar Product of "$\hat{i}+ 2\hat{j}+ 3\hat{k} \: and \: 2\hat{i}- 5\hat{j}+ \hat{k}$" is ' - 5'.

Know More :-

Scalar Product (or) Dot Product :-  If the product of two vectors produces a scalar, such product is called Scalar product (or) Dot product.

The dot Product of two vectors is the product of the magnitudes of the vectors and cosine of angle between them.