If a=hat{i}-2 hat{j}-3 hat{k}, b=2 hat{i}+hat | vedclass

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

Question

(A) Given vectors are $a=\hat{i}-2 \hat{j}-3 \hat{k}$,$b=2 \hat{i}+\hat{j}-\hat{k}$,and $c=\hat{i}+3 \hat{j}-2 \hat{k}$.Using the vector triple produc

Vedclass · Accepted Answer

$160000$

Vedclass · Answer

(A) Given vectors are $a=\hat{i}-2 \hat{j}-3 \hat{k}$,$b=2 \hat{i}+\hat{j}-\hat{k}$,and $c=\hat{i}+3 \hat{j}-2 \hat{k}$.Using the vector triple product identity $(u 	imes v) 	imes w = (u \cdot w)v - (v \cdot w)u$,we have:$(a 	imes b) 	imes (b 	imes c) = [a b c]b$$(b 	imes c) 	imes (c 	imes a) = [b c a]c = [a b c]c$$(c 	imes a) 	imes (a 	imes b) = [c a b]a = [a b c]a$Now,calculate the scalar triple product $[a b c]$:$[a b c] = \begin{vmatrix} 1 & -2 & -3 \ 2 & 1 & -1 \ 1 & 3 & -2 \end{vmatrix} = 1(-2+3) + 2(-4+1) - 3(6-1) = 1 - 6 - 15 = -20$.Let $k = [a b c] = -20$. Then the expression becomes $[kb, kc, ka]$.Using the property of scalar triple products,$[kb, kc, ka] = k^3 [b c a] = k^3 [a b c] = k^3 \cdot k = k^4$.Substituting $k = -20$:$(-20)^4 = 160000$.

If $a=\hat{i}-2 \hat{j}-3 \hat{k}, b=2 \hat{i}+\hat{j}-\hat{k}, c=\hat{i}+3 \hat{j}-2 \hat{k}$,then $[(a \times b) \times(b \times c), (b \times c) \times(c \times a), (c \times a) \times(a \times b)] = $

Similar Questions

If the vectors $a \hat{i}+\hat{j}+\hat{k}$,$\hat{i}+b \hat{j}+\hat{k}$,and $\hat{i}+\hat{j}+c \hat{k}$ are coplanar,where $(a, b, c \neq 1)$,then the value of $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=$

The sum of the distinct real values of $\mu$,for which the vectors $\mu \hat{i} + \hat{j} + \hat{k}$,$\hat{i} + \mu \hat{j} + \hat{k}$,and $\hat{i} + \hat{j} + \mu \hat{k}$ are coplanar,is

For any non-zero vectors $\bar{a}, \bar{b}, \bar{c}$,the value of $\bar{a} \cdot [(\bar{b} \times \bar{c}) \times (\bar{a} + \bar{b} + \bar{c})]$ is

If $A \equiv (1, -1, 0)$,$B \equiv (0, 1, -1)$,and $C \equiv (-1, 0, 1)$,then the unit vector $\overline{d}$ such that $\overline{a}$ and $\overline{d}$ are perpendicular and $\overline{b}, \overline{c}, \overline{d}$ are coplanar is

Let $a=\hat{i}+2 \hat{j}-\hat{k}$ and $b=\hat{i}+\hat{j}+\hat{k}$. If $p$ is a unit vector such that $[a b p]$ is maximum, then $p=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module