If a+b=i and a=2 i-2 j+2 k, then |b| equals: - Vidyadip

MCQ

If $\vec{a}+\vec{b}=\hat{i}$ and $\vec{a}=2 \hat{i}-2 \hat{j}+2 \hat{k}$, then $|\vec{b}|$ equals:

A
$\sqrt{14}$
✓
$3$
C
$\sqrt{12}$
D
$\sqrt{17}$

✓

Answer

Correct option: B.

$3$

$\text {Given, } \hat{a}+\hat{b}=\hat{i} $ and $ \vec{a}=2 \hat{i}-2 \hat{j}+2 \hat{k}$
$\Rightarrow 2 \hat{i}-2 \hat{j}+2 \hat{k}+\vec{b}=\hat{i} $
$\Rightarrow \vec{b}=\hat{i}-(2 \hat{i}-2 \hat{j}+2 \hat{k})$
$\Rightarrow -\hat{i}+2 \hat{j}-2 \hat{k}$
$\therefore|\vec{b}|=\sqrt{(-1)^2+(2)^2+(-2)^2}$
$=\sqrt{1+4+4}$
$=\sqrt{9}$
$=3$

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 Vector Algebra→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

If $A$ is a square matrix of order $3,\left|A^{\prime}\right|=-3$, then $\left|A A^{\prime}\right|=$

${I_1} = \int {{{\sin }^{ - 1}}x\,\,dx} $ and ${I_2} = \int {{{\sin }^{ - 1}}\sqrt {1 - {x^2}} } dx$then

In each of the following, choose the correct answer:
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is

If $f(x) = x + tanx$ and $g(x)$ is inverse of $f(x)$ then $g'(x)$ is equal to

$\int\frac{9\text{x}}{9\text{x}^2+1}=$

Area of one region included between the $sine$ and $cosine$ curves is given by

The normal at the point $(1, 1)$ on the curve $2y + x^2 = 3$ is :

Choose the correct answer from the given four options. The value of the expression $\tan\Big(\frac{1}{2}\cos^{-1}\frac{2}{\sqrt{5}}\Big)$ is: Hint: $\bigg[\tan\frac{\theta}{2}=\sqrt{\frac{1-\cos\theta}{1+\cos\theta}}\bigg]$

If $(0, 0),(a, 0)$ and $(0, b)$ are collinear, then:

Let $f:[-1,2] \rightarrow \mathrm{R}$ be given by $f(x)=2 x^2+x+\left[x^2\right]-[x]$, where $[t]$ denotes the greatest integer less than or equal to $t$. The number of points, where $f$ is not continuous, is :