Question

A and B are two vectors and theta is the angle between them,if |A×B|=√3(A•B) the value of theta is​

Answer 1

ANSWER:

Angle between the vectors = 60°

Step by step explanations:

given that ,

A and B are two vectors and theta is the angle between them

let the two vectors be

A ^ - > and B ^ - >

also given that,

|A ^ -> × B ^ - >| = √3(A ^ - > • B ^ - > )

we know that,

cross product of vector A and B

= AB sinθ

and,

dot product of two vectors

= AB cosθ

According to the question,

|AB sinθ = √3AB cosθ

sinθ = √3 cosθ

sinθ/cosθ = √3

tanθ = √3

so,

θ = 60°

so,

Angle between the vectors

= 60°

Answer 2

Answer:

Angle between the two vectors A And B is 60°.

Explanation:

Given the relation, $\big|\vec A \times \vec B |\big= \sqrt{3} \big(\vec A . \vec B )\big$

On left hand side, it is cross product of two vectors, therefore

                               $\big|\vec A \times \vec B |\big= \big|\vec A |\big\ \big|\vec B |\big sin\theta$

and on right hand, it is the dot product of two vectors, therefore

                                  $\big|\vec A . \vec B |\big= \big|\vec A |\big\ \big|\vec B |\big cos\theta$

Hence,

                                $\big|\vec A \times \vec B |\big= \sqrt{3} \big(\vec A . \vec B )\big$

                  $\implies \big|\vec A |\big\ \big|\vec B |\big sin\theta=\sqrt{3} \big|\vec A |\big\ \big|\vec B |\big cos\theta$

                             $\implies sin\theta = \sqrt{3} cos\theta$

                              $\implies \frac{sin\theta}{cos\theta} = \sqrt{3}$

                              $\implies tan\theta = \sqrt{3}\implies \theta=60^{o}$

Therefore, the angle between the two vectors is 60°.