Find the unit vector parallel to the vector i + 3 j . - Vidyadip

Question

Find the unit vector parallel to the vector $\hat{\text{i}}+\sqrt3\hat{\text{j}}$.

✓

Answer

Let $\vec{\text{a}}=\hat{\text{i}}+\sqrt3\hat{\text{j}}$
Then, $\big|\vec{\text{a}}\big|=\sqrt{1^2+\big(\sqrt3\big)^2}$
$=\sqrt{1+3}$
$=\sqrt4$
$=2$
Unit vector parallel to $\vec{\text{a}}=\hat{\text{a}}=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{1}{2}\big(\hat{\text{i}}+\sqrt3\hat{\text{j}}\big)=\frac{1}2\hat{\text{i}}+\frac{\sqrt3}2\hat{\text{j}}$

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 "2 Marks Questions" from Algebra of Vectors→Algebra of Vectors — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the value of $\sin ^{-1}\left(\cos \frac{3 \pi}{5}\right)$.

Find the value of $\int \operatorname{cosec}^2 x \sec ^2 x \ d x$.

Show that the function $f(x)=x^{100}+\sin x-1$ is increasing on the interval $\left(\frac{\pi}{2}, \pi\right)$

For the following differntial equations verify that the accompanying function is a solution:

Differential equation	Function
$\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}$	$\text{y}=\text{ax}$

Examine the consistency of the system of equations:

Let $f : R \rightarrow R, g : R \rightarrow R$ be two functions defined by $f(x) = x^2 + x + 1$ and $g(x) = 1 - x^2.$ Write fog $(-2).$

By using the properties of definite integrals, evaluate the integral $\int\limits_0^4 {\left| {x - 1} \right|dx} $

Prove that the function defined by f(x) = tan x is a continuous function.

Prove that the function $f(x) = x^3 - 6x^2 + 12x - 18$ is increasing on $R.$

Let $\text{f}:\text{R}-\Big\{-\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be a function defined as $\text{f(x)}=\frac{2\text{x}}{5\text{x}+3}.$ Write $f^{-1}:$ Range of $\text{f}\rightarrow\ \text{R}-\Big\{-\frac{3}{5}\Big\}.$