Question

the angle between two vectors is A=I-5J and B=2I-10J ​

Answer 1

Answer:

Hence, the angle between them is 0°

Answer 2

Given :

Vector A, $A=i-5j$

Vector B, $B=2i-10j$

To find :

Angle between vector A and B.

Solution :

The angle between two vectors can be calculated using formula of dot product such that :

$A{\cdot} B=|A|B|\cos\theta$  ........(1)

Magnitude of A, $|A|=\sqrt{1+(-5)^2} =\sqrt{26}$

Magnitude of B, $|B|=\sqrt{2^2+(-10)^2} =\sqrt{104}$

$A{\cdot} B=(i-5j){\cdot}(2i-10j)\\\\A{\cdot} B=2+50=52$

Equation (1) becomes :

$\cos\theta=\dfrac{A{\cdot}B}{|A||B|}\\\\\cos\theta=\dfrac{52}{\sqrt{26}\times \sqrt{104} }\\\\\cos\theta=1\\\\\theta=0^{\circ}$

So, the angle between vector A and B is 0 degrees.

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Vectors

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