If vec{a}, vec{b}, vec{c} are non-coplanar ve | vedclass

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

Question

(A) Let the scalar triple product be denoted as $[\vec{a}, \vec{b}, \vec{c}] = \vec{a} \cdot (\vec{b} 	imes \vec{c})$.We know that the scalar triple

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Let the scalar triple product be denoted as $[\vec{a}, \vec{b}, \vec{c}] = \vec{a} \cdot (\vec{b} 	imes \vec{c})$.We know that the scalar triple product is cyclic,so $[\vec{a}, \vec{b}, \vec{c}] = [\vec{b}, \vec{c}, \vec{a}] = [\vec{c}, \vec{a}, \vec{b}]$.Also,swapping any two vectors changes the sign: $[\vec{a}, \vec{c}, \vec{b}] = -[\vec{a}, \vec{b}, \vec{c}]$.Given expression: $E = \frac{[\vec{a}, \vec{b}, \vec{c}]}{[\vec{c}, \vec{a}, \vec{b}]} + \frac{[\vec{b}, \vec{a}, \vec{c}]}{[\vec{c}, \vec{a}, \vec{b}]}$.Since $[\vec{c}, \vec{a}, \vec{b}] = [\vec{a}, \vec{b}, \vec{c}]$ and $[\vec{b}, \vec{a}, \vec{c}] = -[\vec{a}, \vec{b}, \vec{c}]$,$E = \frac{[\vec{a}, \vec{b}, \vec{c}]}{[\vec{a}, \vec{b}, \vec{c}]} + \frac{-[\vec{a}, \vec{b}, \vec{c}]}{[\vec{a}, \vec{b}, \vec{c}]}$.$E = 1 - 1 = 0$.

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors,then $\frac{\vec{a} \cdot (\vec{b} \times \vec{c})}{\vec{c} \cdot (\vec{a} \times \vec{b})} + \frac{\vec{b} \cdot (\vec{a} \times \vec{c})}{\vec{c} \cdot (\vec{a} \times \vec{b})} = \dots$

Similar Questions

For what value of $a$ is the volume of the parallelepiped formed by the vectors $\hat{i} + a\hat{j} + \hat{k}$,$\hat{j} + a\hat{k}$,and $a\hat{i} + \hat{k}$ minimum?

If $a, b, c$ are distinct non-negative numbers and the vectors $a\hat{i} + a\hat{j} + c\hat{k}$, $\hat{i} + \hat{k}$, and $c\hat{i} + c\hat{j} + b\hat{k}$ lie in the same plane, then the value of $c$ is...

$[\hat{i}-\hat{j}, \hat{j}-\hat{k}, \hat{k}-\hat{i}]$ is equal to

The vector $c \cdot (b+c) \times (a+b+c)$ is equal to

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