Find the unit vector in the direction of 3 i +4 j -12 k . - Vidyadip

Question

Find the unit vector in the direction of $3\hat{\text{i}}+4\hat{\text{j}}-12\hat{\text{k}}$.

✓

Answer

Let $\vec{\text{a}}=3\hat{\text{i}}+4\hat{\text{j}}-12\hat{\text{k}}$Then, $\big|\vec{\text{a}}\big|=\sqrt{3^2+4^2+(-12)^2}$
$=\sqrt{9+16+144}$
$=\sqrt{169}$
$=13$
So, a unit vector in the direction of $\vec{\text{a}}$ is given by
$\hat{\text{a}}=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{1}{13}\big(3\hat{\text{i}}+4\hat{\text{j}}-12\hat{\text{k}}\big)$
$=\frac{3}{13}\hat{\text{i}}+\frac{4}{13}\hat{\text{j}}-\frac{12}{13}\hat{\text{k}}$

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

Find the value of a, b, c and d from the following equations:
$\begin{bmatrix}2\text{a}+\text{b}&\text{a}-2\text{b}\\5\text{c}-\text{d}&4\text{c}+3\text{d}\end{bmatrix}=\begin{bmatrix}4&-3\\11&24\end{bmatrix}$

Evaluate the following definite integrals:
$\int_{0}^\limits{\frac{\pi}{2}}\sqrt{1+\cos\text{x}}\text{ dx}$

Evaluate the following:
$\sin\Big(\frac{1}{2}\cos^{-1}\frac{4}{5}\Big)$

If $B$ is a symmetric matrix, write whether the matrix $AB A^T$ is symmetric or skew-symmetric.

Find the vector equation of a plane passing throught a point with position $2\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$ and perpendicular to the vector $4\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}}$

Find the antiderivative $F (x)$ of the function defined by $f(x)=5 x^4-5$ where $F (0)=2$.

Find the equation of the line passing through the points (2, -1, 3) and parallel to the line $\vec{\text{r}}=\big(\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}\big)+\lambda\big(2\hat{\text{i}}+3\hat{\text{j}}-5\hat{\text{k}}\big).$

Answer the following quations in one word or one sentence or as per exact requirement of the question:
Write the distance of a point P(a, b, c) from x-axis.

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$5\frac{\text{d}^2\text{y}}{\text{dx}^2}=\Big\{1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2\Big\}^{\frac{3}{2}}$

Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$