If the vectors a hat{i}+hat{j}+hat{k},hat{i}+ | vedclass

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

Question

(B) Since the vectors are coplanar,their scalar triple product is zero: $\begin{vmatrix} a & 1 & 1 \ 1 & b & 1 \ 1 & 1 & c \end{vmatrix} = 0$ Applyi

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Since the vectors are coplanar,their scalar triple product is zero: $\begin{vmatrix} a & 1 & 1 \ 1 & b & 1 \ 1 & 1 & c \end{vmatrix} = 0$ Applying row operations $R_2 ightarrow R_2 - R_1$ and $R_3 ightarrow R_3 - R_1$: $\begin{vmatrix} a & 1 & 1 \ 1-a & b-1 & 0 \ 1-a & 0 & c-1 \end{vmatrix} = 0$ Expanding along the first row: $a((b-1)(c-1) - 0) - 1((1-a)(c-1) - 0) + 1(0 - (1-a)(b-1)) = 0$ $a(b-1)(c-1) - (1-a)(c-1) - (1-a)(b-1) = 0$ Divide the entire equation by $(1-a)(1-b)(1-c)$ (noting $a, b, c 
eq 1$): $\frac{a(b-1)(c-1)}{(1-a)(1-b)(1-c)} - \frac{(1-a)(c-1)}{(1-a)(1-b)(1-c)} - \frac{(1-a)(b-1)}{(1-a)(1-b)(1-c)} = 0$ $\frac{-a}{(1-a)} - \frac{1}{(1-b)} - \frac{1}{(1-c)} = 0$ Since $\frac{-a}{1-a} = \frac{1-a-1}{1-a} = 1 - \frac{1}{1-a}$,we substitute: $1 - \frac{1}{1-a} - \frac{1}{1-b} - \frac{1}{1-c} = 0$ Therefore,$\frac{1}{1-a} + \frac{1}{1-b} + \frac{1}{1-c} = 1$.

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

Similar Questions

The total number of $RNA$ strands in an animal virus is:

........ of a reaction cannot be determined experimentally.

$A$ bob of mass $m$ attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega \ rad/s$ about the vertical axis. About the point of suspension:

For any integer $n \geq 1$, the number of positive divisors of $n$ is denoted by $d(n)$. Then, for a prime $P$, $d(d(d(P^7)))$ is equal to

Who first discovered protoplast fusion?

Vedclass Test Series

Exam Paper Generator

Online Exam Module