Question

Given two vectors A=3I+4J and B=i+j.theta is the angle between A and B. Which of the following statements is/are correct?

Answer 1

Apply costheta fomula

Answer 2

The angle between vectors is 8.06 degrees.

Explanation:

Vector A, $A=3i+4j$

Vector B, $B=i+j$

We need to find the angle between two vectors. It can be calculated using dot product.

$A{\cdot}B=|A||B|\cos \theta\\\\\cos \theta=\dfrac{A{\cdot} B}{|A||B|}\\\\\cos \theta=\dfrac{(3i+4j){\cdot} (i+j)}{\sqrt{3^2+4^2}\times \sqrt{1^2+1^2} }\\\\\cos\theta=\dfrac{3+4}{7.07}\\\\\cos\theta=\dfrac{7}{7.07}\\\\\theta=8.06^{\circ}$

So, the angle between vectors is 8.06 degrees.

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Vectors

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