If the vectors a=hat{i}-hat{j}+2 hat{k},b=2 h | vedclass

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

Question

(A) Given vectors are $a=\hat{i}-\hat{j}+2 \hat{k}$,$b=2 \hat{i}+4 \hat{j}+\hat{k}$,and $c=\lambda \hat{i}+\hat{j}+\mu \hat{k}$.Since the vectors are

Vedclass · Accepted Answer

$(-3, 2)$

Vedclass · Answer

(A) Given vectors are $a=\hat{i}-\hat{j}+2 \hat{k}$,$b=2 \hat{i}+4 \hat{j}+\hat{k}$,and $c=\lambda \hat{i}+\hat{j}+\mu \hat{k}$.Since the vectors are mutually orthogonal,their dot products are zero:$a \cdot c = 0 \implies (1)(\lambda) + (-1)(1) + (2)(\mu) = 0 \implies \lambda + 2\mu = 1$ ...$(i)$$b \cdot c = 0 \implies (2)(\lambda) + (4)(1) + (1)(\mu) = 0 \implies 2\lambda + \mu = -4$ ...(ii)From equation (ii),we get $\mu = -4 - 2\lambda$.Substituting this into equation $(i)$:$\lambda + 2(-4 - 2\lambda) = 1$$\lambda - 8 - 4\lambda = 1$$-3\lambda = 9 \implies \lambda = -3$.Now,substitute $\lambda = -3$ into $\mu = -4 - 2\lambda$:$\mu = -4 - 2(-3) = -4 + 6 = 2$.Thus,$(\lambda, \mu) = (-3, 2)$.

If the vectors $a=\hat{i}-\hat{j}+2 \hat{k}$,$b=2 \hat{i}+4 \hat{j}+\hat{k}$,and $c=\lambda \hat{i}+\hat{j}+\mu \hat{k}$ are mutually orthogonal,then $(\lambda, \mu)$ is equal to

Similar Questions

In the above figure,$P$ divides $AC$ in the ratio $3:4$ and $Q$ divides $BC$ in the ratio $4:3$. Then $M$ divides $AQ$ in the ratio:

Show that the points $A (2 \hat{i}-\hat{j}+\hat{k})$,$B (\hat{i}-3 \hat{j}-5 \hat{k})$,and $C (3 \hat{i}-4 \hat{j}-4 \hat{k})$ are the vertices of a right-angled triangle.

Let $\bar{a}, \bar{b}, \bar{c}$ be three vectors such that $|\bar{a}|=1, |\bar{c}|=1, |\bar{b}|=4$,and $|\bar{b} \times \bar{c}|=\sqrt{15}$. If $\lambda \bar{a}=\bar{b}-2 \bar{c}$,then the value of $\lambda$ is

If $a$ and $b$ are two unit vectors such that $a+2b$ and $5a - 4b$ are perpendicular to each other,then the angle between $a$ and $b$ is ............. $^o$

If the moduli of $a$ and $b$ are equal and the angle between them is $120^\circ$ and $a \cdot b = -8$,then $|a|$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module