Let a = 3 i + 2 j + 2 k and b = i + 2 j - 2 k be two vectors. If … - Vidyadip

MCQ

Let $\vec a = 3\hat i + 2\hat j + 2\hat k$ and $\vec b = \hat i + 2\hat j - 2\hat k$ be two vectors. If a vector perpendicular to both the vectors $\vec a + \vec b$ and $\vec a - \vec b$ has the magnitude $12$ then one such vector is

✓
$4\,\left( {2\hat i - 2\hat j - \hat k} \right)$
B
$4\,\left( {2\hat i - 2\hat j + \hat k} \right)$
C
$4\,\left( {2\hat i + 2\hat j + \hat k} \right)$
D
$4\,\left( {2\hat i + 2\hat j - \hat k} \right)$

✓

Answer

Correct option: A.

$4\,\left( {2\hat i - 2\hat j - \hat k} \right)$

a
$(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})$

$ = 2\left| {\begin{array}{*{20}{c}}
{\hat i}&{\hat j}&{\hat k}\\
1&2&{ - 2}\\
3&2&2
\end{array}} \right|$

$=2(8 \hat{i}-8 \hat{j}+4 \hat{k})$

$\text { Required vector }=\pm 12 \frac{(2 \hat{i}-2 \hat{j}-\hat{k})}{3}$

$=\pm 4(2 \tilde{i}-2 \hat{j}-\hat{k})$

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

More "M.C.Q (1 Marks)" from STD 12 - 10. vector algebra→STD 12 - 10. vector algebra — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If ${\Delta _1} = \left| {\begin{array}{*{20}{c}}
x&{\sin \,\theta }&{\cos \,\theta } \\
{\sin \,\theta }&{ - x}&1 \\
{\cos \,\theta }&1&x
\end{array}} \right|$ and ${\Delta _1} = \left| {\begin{array}{*{20}{c}}
x&{\sin \,2\theta }&{\cos \,\,2\theta } \\
{\sin \,2\theta }&{ - x}&1 \\
{\cos \,\,2\theta }&1&x
\end{array}} \right|$, $x \ne 0$ ; then for all $\theta \in \left( {0,\frac{\pi }{2}} \right)$

$\frac{d}{{dx}}\left( {{a^{{{\log }_{10}}{\rm{cose}}{{\rm{c}}^{ - 1}}x}}} \right)$=

A particle is moving along the curve $x = a{t^2} + bt + c.$ If $ac = {b^2},$ then the particle would be moving with uniform

Let $\alpha > 0$. If $\int \limits _0^\alpha \frac{ x }{\sqrt{ x +\alpha}-\sqrt{ x }} dx =\frac{16+20 \sqrt{2}}{15}$, then $\alpha$ is equal to :

What is the value of $ {\sin}^{-1}(\sin 160^{\circ})?$

If the order of a matrix is 20 × 5 then the number of elements in the matrix is _____?

If a unit vector $\vec r$ makes angles $\frac{\pi }{3}$ with $\hat i$, $\frac{\pi }{4}$ with $\hat j$ and $\theta \in \left( {0,\pi } \right)$ with $\hat k$, then a value of $\theta$ is

For two events $A$ and $B$, if $P(A)=0.4, P(B)=0.8$ and $P(B / A)=0.6$, then $P(A \cup B)$ is

Choose the correct answer from the given four options.The solution of the differential equation $\frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x}-\text{y}}+\text{x}^2\text{e}^{-\text{y}}$ is :

If $\text{f(x)}=\begin{cases}\frac{\sin(\cos\text{x})-\cos\text{x}}{(\pi-2\text{x})^2},&\text{x}\neq\frac{\pi}{2}\\\text{k},&\text{x}=\frac{\pi}{2}\end{cases}$ is continuous at $\text{x}=\frac{\pi}{2},$ then k is equal to: