If |a| + |b| , = ,|c| and a + b = c, then the angle between a and… - Vidyadip

MCQ

If $|a| + |b|\, = \,|c|$ and $a + b = c,$ then the angle between $ a$ and $ b$ is

A
$\frac{\pi }{2}$
B
$\pi $
✓
$0$
D
None of these

✓

Answer

Correct option: C.

$0$

c
(c) $a + b = c \Rightarrow \,|a{|^2} + |b{|^2} + 2a\,.\,b = \,|c{|^2}$

and $|a| + |b|\, = \,|c|$ $ \Rightarrow \,|a{|^2} + |b{|^2} + 2|a||b|\, = \,|c{|^2}$

$\therefore \,a\,.\,b = \,|a||b| \Rightarrow \cos \theta = 1$

==> $\theta = 0.$

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

If $(\alpha,\beta,\gamma)$ be intersection point of lines $x -3y + 2z + 4 = 0 = 2x + y + 4z + 1$ and $\frac{x-\frac{1}{3}}{8}=\frac{y}{3}=\frac{z}{-1}$, then $\alpha+\beta+\gamma$ is -

Area of the triangle formed by the lines $x -y = 0, x + y = 0$ and any tangent to the hyperbola $x^2 -y^2 = a^2$ is :-

If ${p^{th}},\;{q^{th}},\;{r^{th}}$ and ${s^{th}}$ terms of an $A.P.$ be in $G.P.$, then $(p - q),\;(q - r),\;(r - s)$ will be in

The number of solutions, of the equation $e ^{\sin x }-2 e ^{-\sin x }=2$ is

Let $P \left( x _0, y _0\right)$ be the point on the hyperbola $3 x ^2-4 y ^2$ $=36$, which is nearest to the line $3 x+2 y=1$. Then $\sqrt{2}\left( y _0- x _0\right)$ is equal to :

If ${\tan ^{ - 1}}x + {\cos ^{ - 1}}\frac{y}{{\sqrt {(1 + {y^2})} }} = {\sin ^{ - 1}}\frac{3}{{\sqrt {10} }}$ and both $x$ and $y$ are positive and integral, then $x$ and $y =$

If $\left(\sin ^{-1} x\right)^{2}-\left(\cos ^{-1} x\right)^{2}=a ; 0\,<\,x\,<\,1, a \neq 0$, then the value of $2 \mathrm{x}^{2}-1$ is :

$\int_{}^{} {\frac{1}{{{{\cos }^{ - 1}}x.\sqrt {1 - {x^2}} }}dx = } $

Let $y =\log _{ e }\left(\frac{1- x ^2}{1+ x ^2}\right),-1< x <1$. Then at $x =\frac{1}{2}$, the value of $225\left(y^{\prime}-y^{\prime \prime}\right)$ is equal to

The sum of infinity of a geometric progression is $\frac{4}{3}$ and the first term is $\frac{3}{4}$. The common ratio is