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

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

Similar questions

From any point on the circle ${x^2} + {y^2} = {a^2}$ tangents are drawn to the circle ${x^2} + {y^2} = {a^2}{\sin ^2}\alpha $, the angle between them is

One hundred identical coins each with probability $p$ of showing up heads are tossed once. If $0 < p < 1$ and the probability of heads showing on $50$ coins is equal to that of heads showing on $51$ coins, then the value of $p$ is

The differential coefficient of ${\tan ^{ - 1}}\sqrt x $ with respect to $\sqrt x $ is

Area of the triangle with vertices $(a,b),\;({x_1},{y_1})$ and $({x_2},{y_2})$, where $a,\;{x_1}$ and ${x_2}$ are in $G.P.$ with common ratio r and b, ${y_1}$ and ${y_2}$ are in $G.P.$ with common ratio $s$, is given by

If $A = \{2, 3, 4, 8, 10\}, B = \{3, 4, 5, 10, 12\}, C = \{4, 5, 6, 12, 14\}$ then $(A \cap B) \cup (A \cap C)$ is equal to

Let ${a_1},{a_2},.......,{a_{30}}$ be an $A.P.$, $S = \sum\limits_{i = 1}^{30} {{a_i}} $ and $T = \sum\limits_{i = 1}^{15} {{a_{2i - 1}}} $.If ${a_5} = 27\,a$ and $S - 2T = 75$ , then $a_{10}$ is equal to

For three positive integers $p , q , r , x ^{ pq p ^2}= y ^{ qr }= z ^{ p ^2 r }$ and $r=p q+1$ such that $3,3 \log _y x, 3 \log _z y, 7 \log _x z$ are in A.P. with common difference $\frac{1}{2}$. Then $r - p - q$ is equal to

One maximum point of ${\sin ^p}x{\cos ^q}x$ is

A coin is tossed $m + n$ times, where $m \ge n.$ The probability of getting at least $m$ consecutive heads is

The value of ${\log _3}\,4{\log _4}\,5{\log _5}\,6{\log _6}\,7{\log _7}\,8{\log _8}\,9$ is