Given vectors a, b, c such that a ,.(b c) = 0, , the value of (b … - Vidyadip

Question

Given vectors $a, b, c $ such that $a\,.(b \times c)$$ = \lambda \ne 0,\,$ the value of $(b \times c)\,.\,(a + b + c)/\lambda $ is

✓

Answer

b
(b) $\frac{(b\times c)\,.\,(a+b+c)}{\lambda }$ $=\frac{(b\times c)\,.\,a+(b\times c)\,.\,b+(b\times c)\,.\,c}{\lambda }$

$=\frac{(b\times c)\,.\,a+0+0}{\lambda }$
$ = \frac{\lambda }{\lambda } = 1$,

($\because $ Given $a.\,(b\times c)=\lambda =(b\times c)\,.\,a$)

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $p$ for which the sum of the squares of the roots of equation $x^2 -(p + 3)x + (5p\ -2) = 0$ assume its least value is

From a lot of $10$ items, which include $3$ defective items, a sample of $5$ items is drawn at random. Let the random variable $X$ denote the number of defective items in the sample. If the variance of $X$ is $ \sigma^2$, then $96 \sigma^2$ is equal to $..........$

There are $16$ points in a plane, no three of which are in a straight line except $8$ which are all in a straight line. The number of triangles that can be formed by joining them equals

Line $Ax + By + C = 0$ cuts circle ${x^2} + {y^2} + ax + by + c = 0$ in $P$ and $Q$ and the line $A'x + B'y + C' = 0$ cuts the circle ${x^2} + {y^2} + a'x + b'y + c' = 0$ in $R$ and $S$. If the four points $P, Q, R$ and $S$ are con-cyclic, then $D = \left| {\begin{array}{*{20}{c}}{a - a'}&{b - b'}&{c - c'}\\A&B&C\\{A'}&{B'}&{C'}\end{array}} \right|$ =

Let for $n =1,2, \ldots \ldots, 50, S _{ a }$ be the sum of the infinite geometric progression whose first term is $n ^{2}$ and whose common ratio is $\frac{1}{(n+1)^{2}}$. Then the value of $\frac{1}{26}+\sum\limits_{n=1}^{50}\left(S_{n}+\frac{2}{n+1}-n-1\right)$ is equal to

Let $A:\left\{ {z:{{\left( {\frac{{z - \bar z}}{{2i}}} \right)}^2} \leqslant 2\left( {z - \bar z} \right)} \right\}$ where $i = \sqrt { - 1}$ and $B : \{z : |z| \leqslant \sqrt 5 \}$.Number of points with integral real and imaginary parts of $z$ lying in $A \cap B$ is -

The number of $6-$digit numbers of the form $a b a b a b$ (in base $10$) each of which is a product of exactly $6$ distinct primes is

If ${(r + 1)^{th}}$ term is the first negative term in the expansion of ${(1 + x)^{7/2}}$, then the value of $r$ is

If the fourth term in the expansion of $\left(x+x^{\log _{2} x}\right)^{7}$ is $4480,$ then the value of $x$ where $x \in N$ is equal to

Let $B$ be the centre of the circle $x^{2}+y^{2}-2 x+4 y+1=0$ Let the tangents at two points $\mathrm{P}$ and $\mathrm{Q}$ on the circle intersect at the point $\mathrm{A}(3,1)$. Then $8.$ $\left(\frac{\text { area } \triangle \mathrm{APQ}}{\text { area } \triangle \mathrm{BPQ}}\right)$ is equal to .... .