If be the angle between the unit vectors a and b, then a - 2 ,b w… - Vidyadip

MCQ

If $\theta$ be the angle between the unit vectors $a$ and $b$, then $a - \sqrt 2 \,b$ will be a unit vector if $\theta = $

A
$\frac{\pi }{6}$
✓
$\frac{\pi }{4}$
C
$\frac{\pi }{3}$
D
$\frac{{2\pi }}{3}$

✓

Answer

Correct option: B.

$\frac{\pi }{4}$

b
(b) ${(a - \sqrt 2 b)^2} = 1 \Rightarrow 1 + 2 - 2\sqrt 2 a\,.\,b = 1$

$ \Rightarrow a\,.\,b = \frac{1}{{\sqrt 2 }} \Rightarrow \cos \theta = \frac{1}{{\sqrt 2 }} \Rightarrow \theta = \frac{\pi }{4}.$

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

Three numbers are chosen at random, one after another with replacement, from the set $S=\{1,2,3, \ldots, 100\}$. Let $p_1$ be the probability that the maximum of chosen numbers is at least 81 and $p _2$ be the probability that the minimum of chosen numbers is at most $40$ .

($1$) The value of $\frac{625}{4} p _1$ is

($2$) The value of $\frac{125}{4} p _2$ is

Give the answer or queution ($1$) and ($2$)

The value of a so that the sum of the squares of the roots of the equation ${x^2} - (a - 2)x - a + 1 = 0$ assume the least value, is

The area bounded by the curve y²= 8x, the x-axis and the lastus rectum is:

$\frac{16}{3}$
$\frac{23}{3}$
$\frac{32}{3}$
$\frac{16\sqrt{2}}{3}$

The value of the integral $\int \limits_1^2\left(\frac{t^4+1}{t^6+1}\right) d t$ is $..........$.

The ratio in which 2x + 3y + 5z = 1 divides the line joining the points (1, 0, -3) and (1, -5, 7) is:

5 : 3
3 : 2
2 : 1
1 : 3

Let $R$ be a relation defined on $N$ as a $R$ b is $2 a+3 b$ is a multiple of $5, a, b \in N$. Then $R$ is

An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is,

$\int\frac{\text{dx}}{1-\cos\text{x}-\sin\text{x}}$ is equal to:

$\log|1+\cot\frac{\text{x}}{2}|+\text{c}$
$\log|1-\tan\frac{\text{x}}{2}|+\text{c}$
$\log|1-\cot\frac{\text{x}}{2}|+\text{c}$
$\log|1+\tan\frac{\text{x}}{2}|+\text{c}$

The area of the region $\{(\text{x},\text{y}):\text{x}^2+\text{y}^2\leq1\leq\text{x}+\text{y}\}$ is:

$\frac{\pi}{5}$
$\frac{\pi}{4}$
$\frac{\pi}{2}-\frac{1}{2}$
$\frac{\pi^2}{2}$

${x_1} + 2{x_2} + 3{x_3} = a2{x_1} + 3{x_2} + {x_3} = $ $b3{x_1} + {x_2} + 2{x_3} = c$ this system of equations has