If (a b)^2 + (a , ,. , ,b)^2 = 144 and |a| , = 4, then |b| , = - Vidyadip

MCQ

If ${(a \times b)^2} + {(a\,\,.\,\,b)^2} = 144$ and $|a|\, = 4,$ then $|b|\, = $

A
$16$
B
$8$
✓
$3$
D
$12$

✓

Answer

Correct option: C.

$3$

c
(c) We know that ${(a \times b)^2} + {(a\,.\,b)^2} = \,|a{|^2}|b{|^2}$

$\therefore \,\,\,144 = 16|b{|^2} \Rightarrow \,|b| = 3.$

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 10. vector algebra→10. vector algebra — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let R be a relation on N defined by x + 2y = 8. The domain of R is:

{2, 4, 8}
{2, 4, 6, 8}
{2, 4, 6}
{1, 2, 3, 4}

What are the direction ratios of normal to the plane 2x - y + 2z + 1 = 0:

(2, -1, 2)
$\big(1,\frac{1}{2},1\big)$
(1, -2, 1)
None of the above

The co-ordinates of the foot of perpendicular drawn from point $P(1,0,3)$ to the join of points $A(4,7,1)$ and $B(3,5,3)$ is

The optimal value of the objective function is attained at the points

Let f(x) = (x + |x|) |x|. Then, for all x:

f is continuous.
f is differentiable for some x
f' is continuous.
f'' is continuous.

Let $a = i$ be a vector which makes an angle of ${120^o}$ with a unit vector $b$ Then the unit vector $(a + b)$ is

If $f(x) = \left\{ \begin{array}{l}\frac{{{x^4} - 16}}{{x - 2}},\,\,{\rm{when}}\,\,x \ne 2\\\,\,\,\,\,\,\,\,\,\,\,\,\,16,\,{\rm{when}}\,\,x = 2\end{array} \right.$, then

Let R be a relation on the set N given by R = {(a, b): a = b - 2, b > 6}. Then,

(2, 4) ∈ R
(3, 8) ∈ R
(6, 8) ∈ R
(8, 7) ∈ R

Let a function $f: N \rightarrow N$ be defined by

$f ( n )=\left[\begin{array}{ll}2 n , \,\,\, \,\,\,\,\,\,n =2,4,6,8, \ldots . \\ n -1,\,\,\, n =3,7,11,15, \ldots . \\ \frac{ n +1}{2}, \,\,\, \,\,\,n =1,5,9,13, \ldots \ldots\end{array}\right.$

then, $f$ is

The value of the integral $\int_{-\pi}^\pi \frac{\cos ^2 x}{1+a^x} d x$, where $a > 0$, is