If overline{a}, overline{b}, overline{c} are | vedclass

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

Question

(C) Given that $\overline{a}, \overline{b}, \overline{c}$ are non-coplanar vectors,the scalar triple product $[\overline{a} \overline{b} \overline{c}]

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) Given that $\overline{a}, \overline{b}, \overline{c}$ are non-coplanar vectors,the scalar triple product $[\overline{a} \overline{b} \overline{c}] 
eq 0$. We know that $\overline{a} \cdot \overline{p} = \overline{a} \cdot \frac{\overline{b} 	imes \overline{c}}{[\overline{a} \overline{b} \overline{c}]} = \frac{[\overline{a} \overline{b} \overline{c}]}{[\overline{a} \overline{b} \overline{c}]} = 1$. Similarly,$\overline{b} \cdot \overline{q} = \overline{b} \cdot \frac{\overline{c} 	imes \overline{a}}{[\overline{a} \overline{b} \overline{c}]} = \frac{[\overline{b} \overline{c} \overline{a}]}{[\overline{a} \overline{b} \overline{c}]} = 1$. And $\overline{c} \cdot \overline{r} = \overline{c} \cdot \frac{\overline{a} 	imes \overline{b}}{[\overline{a} \overline{b} \overline{c}]} = \frac{[\overline{c} \overline{a} \overline{b}]}{[\overline{a} \overline{b} \overline{c}]} = 1$. Substituting these values into the expression: $2 \overline{a} \cdot \overline{p} + \overline{b} \cdot \overline{q} + \overline{c} \cdot \overline{r} = 2(1) + 1 + 1 = 4$.

Similar Questions

The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i + j$ and a vector $b_2$ perpendicular to $a$. Then $b_1 = $

If $x$ and $y$ are two unit vectors and $\theta$ is the angle between them,then $\frac{1}{2}|x-y|$ is equal to

If $a, b$ and $c$ are non-coplanar unit vectors such that the angle between any two of them is $60^\circ$, and the vector $d = xa + yb + zc$ is perpendicular to both $a$ and $b$, then the value of $\frac{(x + y)}{z}$ is

If the position vectors of the vertices of a triangle are $2 \hat{i}-\hat{j}+\hat{k}$,$\hat{i}-3 \hat{j}-5 \hat{k}$,and $3 \hat{i}-4 \hat{j}-4 \hat{k}$,then the triangle is

Let $\bar{a} = 4\bar{i} + 3\bar{j}$ and $\bar{b}$ be two perpendicular vectors in the $XOY$-plane. $A$ vector $\bar{c}$ in the same plane and having projections $1$ and $2$ respectively on $\bar{a}$ and $\bar{b}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module