Find a unit vector in the direction of a =2 i -3 j +6 k . - Vidyadip

Question

Find a unit vector in the direction of $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}$.

✓

Answer

Given:
$\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}$
$|\vec{\text{a}}|=\sqrt{2^2+(-3)^2+6^2}$
$=\sqrt{4+9+36}$
$=\sqrt{49}$
$=7$
Unit vector $=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{2\hat{\text{i}}-3\hat{\text{j}}+6\hat{\text{k}}}{7}$
$=\frac{2}7\hat{\text{i}}-\frac{3}7\hat{\text{j}}+\frac{6}7\hat{\text{k}}$

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 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 $A = [A_{ij}]$ is a $3 \times 3$ diaginal matrix such that $a_{11} = 1, a_{22} = 2, a_{33} = 3,$ then find $|A|.$

Give an example of a relation which is reflexive and transitive but not symmetric.

Find the maximum and minimum value, f(x) = |x + 2| - 1

Evaluate the following:
$\cot^{-1}\frac{1}{\sqrt3}-\text{cosec}^{-1}(-2)+\sec^{-1}\Big(\frac{2}{\sqrt3}\Big)$

Find $\vec{\text{a}}.\vec{\text{b}}$ when
$\vec{\text{a}}=\hat{\text{j}}-\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+3\hat{\text{j}}-2\hat{\text{k}}$

Write the function in the simplest form: ${\tan ^{ - 1}}\sqrt {\frac{{1 - \cos x}}{{1 + \cos x}}} ,\;0<x < \pi $

If $\begin{bmatrix}\text{xy}&4\\\text{z}+6&\text{x}+\text{y}\end{bmatrix}=\begin{bmatrix}8&\text{w}\\0&6\end{bmatrix},$ then find the values of $x, y, z$ and $w$.

If $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ are mutually perpendicular unit vectors, write the value of $\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|.$

Write the direction cosines of the vector $\vec{\text{r}}=6\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$.

Evaluate the following determinant:
$\begin{vmatrix}67&19&21\\39&13&14\\81&24&26 \end{vmatrix}$