If the adjacent sides of a rectangle are bar{ | vedclass

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

Question

(A) Given vectors are $\bar{a}=5\bar{m}-3\bar{n}$,$\bar{c}=-4\bar{m}-\bar{n}$,and $\bar{d}=-\bar{m}+\bar{n}$.First,calculate $\bar{x}$:$\bar{x} = \fra

Vedclass · Accepted Answer

$\frac{\pi}{2}$

Vedclass · Answer

(A) Given vectors are $\bar{a}=5\bar{m}-3\bar{n}$,$\bar{c}=-4\bar{m}-\bar{n}$,and $\bar{d}=-\bar{m}+\bar{n}$.First,calculate $\bar{x}$:$\bar{x} = \frac{\bar{a}+\bar{c}+\bar{d}}{3} = \frac{(5\bar{m}-3\bar{n}) + (-4\bar{m}-\bar{n}) + (-\bar{m}+\bar{n})}{3} = \frac{0\bar{m}-3\bar{n}}{3} = -\bar{n}$.Next,calculate $\bar{y}$:$\bar{y} = \frac{\bar{c}+\bar{d}}{5} = \frac{(-4\bar{m}-\bar{n}) + (-\bar{m}+\bar{n})}{5} = \frac{-5\bar{m}}{5} = -\bar{m}$.Since $\bar{m}$ and $\bar{n}$ are adjacent sides of a rectangle,they are perpendicular,so $\bar{m} \cdot \bar{n} = 0$. Assuming $|\bar{m}| = |\bar{n}| = 1$ for simplicity as they represent unit directions of the rectangle sides,the angle $	heta$ between $\bar{x} = -\bar{n}$ and $\bar{y} = -\bar{m}$ is the same as the angle between $\bar{n}$ and $\bar{m}$,which is $\frac{\pi}{2}$.

Similar Questions

If either vector $\vec{a}=\vec{0}$ or $\vec{b}=\vec{0},$ then $\vec{a} \cdot \vec{b}=0 .$ But the converse need not be true. Justify your answer with an example.

The position vectors of the vertices of $\triangle ABC$ are $4\hat{i} - 2\hat{j}$,$\hat{i} + 4\hat{j} - 3\hat{k}$,and $-\hat{i} + 5\hat{j} + \hat{k}$ respectively. Then,$m \angle ABC = $

Find the angle between the lines whose direction ratios are $a, b, c$ and $b-c, c-a, a-b$. (in $^{\circ}$)

If $a$ and $b$ are two vectors,then $(a \times b)^2$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module