Question

Example 2.6: Find the scalar product of the
two vectors
V, =i+2j +3k and v, = 3 i +4j-5 k
​

Answer 1

v1 = i + 2j + 3k

v2 = 3i + 4j - 5k

v1.v2 = (3)(1) + (2)(4) + (3)(-5)

= 3 + 8 - 15

= 11 - 15

= -4

Answer 2

Given :-

${v_1 = \hat{i} + 2\hat{j} + 3\hat{k}}$

${v_2 = 3\hat{i} + 4\hat{j} +-5 \hat{k}}$

To find :-

Dot product

Solution:-

Dot product of ${v_1 = \hat{i} + 2\hat{j} + 3\hat{k}}$ and ${v_2 = 3\hat{i} + 4\hat{j} + -5\hat{k}}$ is

Just we have to multiply numericals no need to multiply ${\hat{i}}$ or ${\hat{j}}$

= 1(3) + 2(4) + 3(-5)

= 3 + 8 - 15

= 11 - 15

= -4

So, the dot product of ${\hat{i} +2\hat{j} +3\hat{k}}$ and ${3\hat{i} + 4\hat{j} + -5\hat{k}}$ is -4

Know more :-

Know more about Dot product :-

If the product of two vectors is again scalar such product is called dot product

Dot product or scalar product both are same

Properties of dot product :-

It obeys commutative law , distributive law

Commutative property :-

$\bar{a} \times \bar{b} = \bar{b} \times \bar{a}$

Distributive property:-

${ \bar a \times ( \bar b + \bar c ) = \bar a \: \bar b + \bar a \: \bar c}$