If |a b| , = 4 and |a ,. ,b| , = 2, then |a |^2 , ,|b |^2 = - Vidyadip

Question

If $|a \times b|\, = 4$ and $|a\,.\,b|\, = 2$, then $|a{|^2}\,\,|b{|^2} = $

✓

Answer

d
(d) Given $|a \times b|\, = 4$ $ \Rightarrow \left| {\,|a||b|\sin \theta \,\,\hat n} \right| = 4$
$ \Rightarrow \left| {\,|a||b|\sin \theta \,} \right| = 4$ …..$(i)$
Also $|a\,.\,b|\, = 2$ $ \Rightarrow \left| {\,|a||b|\cos \theta \,} \right| = 2$
$ \Rightarrow \left| {\,|a||b|\cos \theta \,} \right| = 2$ …..$(ii)$
Now squaring and adding equation $(i)$ and $(ii),$ we get
$|a{|^2}\,.\,|b{|^2}{\sin ^2}\theta \, + |a{|^2}\,.\,|b{|^2}{\cos ^2}\theta = {4^2} + {2^2}$
$\therefore \,|a{|^2}\,.\,|b{|^2}({\sin ^2}\theta + {\cos ^2}\theta ) = 16 + 4$
$ \Rightarrow \,|a{|^2}\,.\,|b{|^2} \times \,1 = 20.$

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 $'a' (a>0)$ for which the area bounded by the curves $y = \frac{x}{6}\, + \,\frac{1}{{{x^2}}} \, , y = 0, x = a$ and $x = 2a$ has the least value, is

The area of the region enclosed between the parabolas $y ^{2}=2 x -1$ and $y ^{2}=4 x -3$ is

Let $S=\left\{z \in C : z^{2}+\bar{z}=0\right\}$. Then $\sum \limits_{z \in S}(\operatorname{Re}(z)+\operatorname{Im}(z))$ is equal to$......$

Let $A=\left(\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right)$. Let $\alpha, \beta \in R$ be such that $\alpha A^{2}+\beta A=2 I$. Then $\alpha+\beta$ is equal to -

Let $\left\{a_{n}\right\}_{n=0}^{\infty}$ be a sequence such that $a_{0}=a_{1}=0$ and $a_{ n +2}=3 a_{ n +1}-2 a_{ n }+1, \forall n \geq 0$.Then $a_{25} a_{23}-2 a_{25} a_{22}-2 a_{23} a_{24}+4 a_{22} a_{24}$ is equal to.

The value of $\sqrt {(\log _{0.5}^24)} $ is

If the orthocentre of the triangle formed by the lines $2 x+3 y-1=0, x+2 y-1=0$ and $a x+b y-1=0$, is the centroid of another triangle, whose circumecentre and orthocentre respectively are $(3,4)$ and $(-6,-8)$, then the value of $|a-b|$ is $..........$

The number of all $3 \times 3$ matrices $A$, with enteries from the set $\{-1,0,1\}$ such that the sum of the diagonal elements of $\mathrm{AA}^{\mathrm{T}}$ is $3,$ is

The mean age of $25$ teachers in a school is $40\, years$. A teacher retires at the age of $60\, years$ and a new teacher is appointed in his place. If now the mean age of the teachers in this school is $39\, years$, then the age (in years) of the newly appointed teacher is

A particle is moving in a straight line according as $s = 45\,t + 11{t^2} - {t^3}$ then the time when it will come to rest, is ......... $\sec$.