Let bar{u}, bar{v}, bar{w} be vectors such th | vedclass

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

Question

(C) Given $|\bar{u}|=1, |\bar{v}|=2, |\bar{w}|=3$. Since the projection of $\bar{v}$ on $\bar{u}$ is equal to the projection of $\bar{w}$ on $\bar{u}$

Vedclass · Accepted Answer

$\sqrt{14}$

Vedclass · Answer

(C) Given $|\bar{u}|=1, |\bar{v}|=2, |\bar{w}|=3$. Since the projection of $\bar{v}$ on $\bar{u}$ is equal to the projection of $\bar{w}$ on $\bar{u}$,we have $\frac{\bar{v} \cdot \bar{u}}{|\bar{u}|} = \frac{\bar{w} \cdot \bar{u}}{|\bar{u}|}$. Since $|\bar{u}|=1$,this implies $\bar{v} \cdot \bar{u} = \bar{w} \cdot \bar{u}$,or $(\bar{v}-\bar{w}) \cdot \bar{u} = 0$. Also,$\bar{v} \perp \bar{w}$ implies $\bar{v} \cdot \bar{w} = 0$. We need to calculate $|\bar{u}-\bar{v}+\bar{w}|^2 = (\bar{u}-\bar{v}+\bar{w}) \cdot (\bar{u}-\bar{v}+\bar{w})$. $= |\bar{u}|^2 + |\bar{v}|^2 + |\bar{w}|^2 - 2(\bar{u} \cdot \bar{v}) + 2(\bar{u} \cdot \bar{w}) - 2(\bar{v} \cdot \bar{w})$. Since $\bar{u} \cdot \bar{v} = \bar{u} \cdot \bar{w}$ and $\bar{v} \cdot \bar{w} = 0$,the terms $-2(\bar{u} \cdot \bar{v}) + 2(\bar{u} \cdot \bar{w})$ cancel out. $= |\bar{u}|^2 + |\bar{v}|^2 + |\bar{w}|^2 = 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14$. Therefore,$|\bar{u}-\bar{v}+\bar{w}| = \sqrt{14}$.

Let $\bar{u}, \bar{v}, \bar{w}$ be vectors such that $|\bar{u}|=1, |\bar{v}|=2, |\bar{w}|=3$. If the projection of $\bar{v}$ on $\bar{u}$ is equal to that of $\bar{w}$ on $\bar{u}$,and the vectors $\bar{v}, \bar{w}$ are perpendicular to each other,then $|\bar{u}-\bar{v}+\bar{w}|=$

Similar Questions

For any two vectors $\vec{a}$ and $\vec{b}$,$|\vec{a}| |\vec{b}|$ . . . . . . $|\vec{a} \cdot \vec{b}|$.

The projection of $\bar{a} = \hat{i} - 2\hat{j} + \hat{k}$ on $\bar{b} = 2\hat{i} - \hat{j} + \hat{k}$ is

If $D$ and $E$ are the midpoints of the sides $BA$ and $BC$ of triangle $ABC$, then $AE + DC =$

If $|a+b|^{2}+|a \cdot b|^{2}=144$ and $|a|=6$,then $|b|$ is equal to

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a}+\vec{b}+\vec{c}=\vec{0},$ find the value of $\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}.$

Vedclass Test Series

Exam Paper Generator

Online Exam Module