Two vectors of same magnitude act at a point. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the magnitude of the two vectors be $A$ and $B$. Given that they have the same magnitude,let $A = B = x$.The resultant magnitude $R$ is given

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(C) Let the magnitude of the two vectors be $A$ and $B$. Given that they have the same magnitude,let $A = B = x$.The resultant magnitude $R$ is given by the formula $R^2 = A^2 + B^2 + 2AB \cos 	heta$,where $	heta$ is the angle between the vectors.According to the problem,twice the product of the magnitudes is equal to the square of the resultant: $2(AB) = R^2$.Substituting $A = x$ and $B = x$,we get $2(x \cdot x) = x^2 + x^2 + 2(x \cdot x) \cos 	heta$.This simplifies to $2x^2 = 2x^2 + 2x^2 \cos 	heta$.Subtracting $2x^2$ from both sides,we get $0 = 2x^2 \cos 	heta$.Since $x 
eq 0$,we must have $\cos 	heta = 0$.Therefore,$	heta = 90^{\circ}$.

Two vectors of same magnitude act at a point. Twice the product of the magnitudes of two vectors is equal to the square of the magnitude of their resultant. The angle between the two vectors is (in $^{\circ}$)

Similar Questions

If $\vec{A}$ and $\vec{B}$ are two non-zero vectors such that $|\vec{A} + \vec{B}| = \frac{|\vec{A} - \vec{B}|}{2}$ and $|\vec{A}| = 2|\vec{B}|$,then the angle between $\vec{A}$ and $\vec{B}$ is

At what angle should the two forces $2P$ and $\sqrt{2}P$ act so that the resultant force is $P\sqrt{10}$ (in $^{\circ}$)?

Two vectors $\vec{A}$ and $\vec{B}$ are parallel to each other if one is a scalar multiple of the other,i.e.,$\vec{A} = k\vec{B}$. Which of the following pairs of vectors are parallel?

Can you associate vectors with $(a)$ the length of a wire bent into a loop,$(b)$ a plane area,$(c)$ a sphere? Explain.

The resultant of $\vec{A}$ and $\vec{B}$ makes an angle $\alpha$ with $\vec{A}$ and $\beta$ with $\vec{B}$. Which of the following is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module