Let vec{a}=hat{i}+hat{j}+hat{k},vec{b}=hat{i} | vedclass

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

Question

(C) Let $\vec{v} = \lambda \vec{a} + \mu \vec{b}$.Substituting the vectors $\vec{a}$ and $\vec{b}$,we get $\vec{v} = \lambda(\hat{i} + \hat{j} + \hat{

Vedclass · Accepted Answer

$3 \hat{i}-\hat{j}+3 \hat{k}$

Vedclass · Answer

(C) Let $\vec{v} = \lambda \vec{a} + \mu \vec{b}$.Substituting the vectors $\vec{a}$ and $\vec{b}$,we get $\vec{v} = \lambda(\hat{i} + \hat{j} + \hat{k}) + \mu(\hat{i} - \hat{j} + \hat{k}) = (\lambda + \mu)\hat{i} + (\lambda - \mu)\hat{j} + (\lambda + \mu)\hat{k}$.The projection of $\vec{v}$ on $\vec{c}$ is given by $\frac{\vec{v} \cdot \vec{c}}{|\vec{c}|} = \frac{1}{\sqrt{3}}$.Given $\vec{c} = \hat{i} - \hat{j} - \hat{k}$,we have $|\vec{c}| = \sqrt{1^2 + (-1)^2 + (-1)^2} = \sqrt{3}$.Thus,$\frac{(\lambda + \mu)(1) + (\lambda - \mu)(-1) + (\lambda + \mu)(-1)}{\sqrt{3}} = \frac{1}{\sqrt{3}}$.$\Rightarrow \lambda + \mu - \lambda + \mu - \lambda - \mu = 1$.$\Rightarrow \mu - \lambda = 1$,or $\mu = \lambda + 1$.Substituting $\mu$ back into $\vec{v}$,we get $\vec{v} = (2\lambda + 1)\hat{i} - \hat{j} + (2\lambda + 1)\hat{k}$.For $\lambda = 1$,we get $\vec{v} = 3\hat{i} - \hat{j} + 3\hat{k}$,which matches option $C$.

$X = x_i$	$-2$	$-1$	$0$	$1$	$2$
$P(X = x_i)$	$\frac{1}{6}$	$k$	$\frac{1}{4}$	$k$	$\frac{1}{6}$

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}$,$\vec{b}=\hat{i}-\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. $A$ vector $\vec{v}$ in the plane of $\vec{a}$ and $\vec{b}$,whose projection on $\vec{c}$ is $\frac{1}{\sqrt{3}}$,is given by

Similar Questions

The species having tetrahedral shape is

If the electric flux entering and leaving a closed surface are $\phi_1$ and $\phi_2$ respectively,then the electric charge inside the surface will be:

The input resistance of a common emitter transistor amplifier,if the output resistance is $500 \, k\Omega$,the current gain $\alpha = 0.98$ and power gain is $6.0625 \times 10^6$,is....$\Omega$

$A$ random variable $X$ has the following probability distribution:
$X = x_i$ $-2$ $-1$ $0$ $1$ $2$
$P(X = x_i)$ $\frac{1}{6}$ $k$ $\frac{1}{4}$ $k$ $\frac{1}{6}$

The variance of this random variable is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module