If a, b and c are non-coplanar,then the value | vedclass

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

Question

(C) Given that $a, b, c$ are non-coplanar,so the scalar triple product $[a b c] 
eq 0$. We know that $[a b c] = [b c a] = [c a b]$. Let $V = [a b c]$

Vedclass · Accepted Answer

$-\frac{1}{6}$

Vedclass · Answer

(C) Given that $a, b, c$ are non-coplanar,so the scalar triple product $[a b c] 
eq 0$. We know that $[a b c] = [b c a] = [c a b]$. Let $V = [a b c]$. The expression is $E = a \cdot \left\{ \frac{b 	imes c}{3 b \cdot (c 	imes a)} ight\} - b \cdot \left\{ \frac{c 	imes a}{2 c \cdot (a 	imes b)} ight\}$. Using the definition of scalar triple product,$b \cdot (c 	imes a) = [b c a] = [a b c] = V$ and $c \cdot (a 	imes b) = [c a b] = [a b c] = V$. Substituting these into the expression: $E = \frac{a \cdot (b 	imes c)}{3 [a b c]} - \frac{b \cdot (c 	imes a)}{2 [a b c]}$ $E = \frac{[a b c]}{3 [a b c]} - \frac{[b c a]}{2 [a b c]}$ Since $[a b c] = [b c a] = V$,we have: $E = \frac{V}{3V} - \frac{V}{2V} = \frac{1}{3} - \frac{1}{2} = \frac{2 - 3}{6} = -\frac{1}{6}$.

If $a, b$ and $c$ are non-coplanar,then the value of $a \cdot \left\{ \frac{b \times c}{3 b \cdot (c \times a)} \right\} - b \cdot \left\{ \frac{c \times a}{2 c \cdot (a \times b)} \right\}$ is

Similar Questions

If $a, b, c$ are any three vectors and their reciprocal vectors are $a^{-1}, b^{-1}, c^{-1}$ such that $[a, b, c] \neq 0$,then $[a^{-1}, b^{-1}, c^{-1}]$ is equal to:

Let $\vec{a}, \vec{b}, \vec{c}$ be unit vectors such that $\vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{c} = \vec{c} \cdot \vec{a} = \cos \theta$. Then the maximum value of $\theta$ is,where $\theta \in [0, \pi]$.

If $\bar{a}$,$\bar{b}$,and $\bar{c}$ are non-coplanar vectors and $(\bar{a} + \bar{b} + \bar{c}) \cdot (\bar{a} \times \bar{b} + \bar{b} \times \bar{c} + \bar{c} \times \bar{a}) = k[\bar{a} \bar{b} \bar{c}]$,then the value of $k$ 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 the vectors $m \hat{i} + m \hat{j} + n \hat{k}$,$\hat{i} + \hat{k}$,and $n \hat{i} + n \hat{j} + p \hat{k}$ lie in a plane,then...

Vedclass Test Series

Exam Paper Generator

Online Exam Module