Question

If A + B = C and A = √3, B = √3 and C = 3, then angle between vectors A and B is ........... .
(A) 0°
(B) 30°
(C) 60°
(D) 90°

Answer 1

the angle between these two vector bevome 60°

Answer 2

Concept

A term having direction and magnitude is known as vector

Given

The equation given is Vector A + Vector B = C

The values of A , B and C given are

$\sqrt{3}$

and

$\sqrt{3} \: and \: 3$

Find

We need to find the angle between A and B

Solution

As we know that the Values of A , B and C are given

So the equation is Vector A+ Vector B = Vector C

Now We will square both the sides

That is mod (Vector A+ VectorB)^2 = mod (Vector C)^2

Now applying the formula for the general equation

Mod Vector A^2 + Mod Vector B^2 + 2 Vector A Vector B cos theta = Mod C^2

Now substitute the values of Vector A , Vector B and Vector C

$3 + 3 + 2( \sqrt{3})( \sqrt{3})$

cos theta = (3)^2

6+6 cos theta = 9

1+ cos theta = 9/6

cos theta = 9/6-1

cos theata = 1/2

theta = 60°

Hence the angle between A vector and B vector is 60°

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