Question

find a vector b vector c vector when a vector = 2j +j+3k, b vector = -i+2j+k and c vector = -3i+j+2j.​

Answer 1

Given to find the dot product :-

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

$B = -\hat{i} +2\hat{j} +\hat{k}$

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

SOLUTION :-

$A.B.C =( 2\hat{i} +\hat{j} + 3\hat{k})(-\hat{i} +2\hat{j} +\hat{k})( -3\hat{i} +\hat{j} + 2\hat{k})$

For finding the dot product Its just enough to multiply only numericals .No need to multiply the $\hat{i} \: or\: \hat{j}\: or \:\hat{k}$

So, the dot product is

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

$= 2(3)+1(2)+3(2)$

$= 6+2+6$

$= 14$

So, the dot product  is 14

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

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