Find the magnitude of a = (3 k +4 j ) ( i + j - k ). - Vidyadip

Question

Find the magnitude of $\vec{\text{a}}=\big(3\hat{\text{k}}+4\hat{\text{j}}\big)\times(\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}).$

✓

Answer

$\vec{\text{a}}=\big(0\hat{\text{i}}+4\hat{\text{j}}+3\hat{\text{k}}\big)\times\big(\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}\big)$
$=\begin{vmatrix}\hat{\text{i}}&\hat{\text{j}}&\hat{\text{k}}\\0&4&3\\1&1&-1 \end{vmatrix}$
$=\hat{\text{i}}(-4-3)-\hat{\text{j}}(0-3)+\hat{\text{k}}(0-4)$
$=-7\hat{\text{i}}+3\hat{\text{j}}-4\hat{\text{k}}$
$\Rightarrow|\vec{\text{a}}|=\sqrt{(-7)^2+3^2+(-4)^2}$
$=\sqrt{74}$

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 "3 Marks Question" from Vector or Cross Product→Vector or Cross Product — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

An unbiased die is thrown twice. A success is getting a number greater than 4. Find the probability distribution of the number of successes.

Write the following function in the simplest form:
$\tan^{-1}\bigg(\frac{\cos x-\sin x}{\cos x+\sin x}\bigg), x<{\pi}$

Let $\vec{\text{a}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}},\vec{\text{b}}=\hat{\text{i}}$ and $\vec{\text{c}}=\text{c}_1\hat{\text{i}}+\text{c}_2\hat{\text{j}}+\text{c}_3\hat{\text{k}}.$ Then,
If $C_2 = -1$ and $C_3 = 1$, show that no value of $C_1$ can make $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ coplanar.

An urn contains 4 red and 7 blue balls. Two balls are drawn at random with replacement. Find the probability of getting:

2 red balls.
2 blue balls.
One red and one blue ball.

Find the value of x if the area of $\triangle$ is $35$ square cms with vertices $(x, 4), (2, -6)$ and $(5, 4)$.

Write the vector equation of the line passing through the point (1, -2, -3) and normal to the plane $\vec{\text{r}}.(2\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}})=5.$

Find the mean and standard deviation of the following probability distributions:

$\text{x}_\text{i}$	$-5$	$-4$	$1$	$2$
$\text{p}_\text{i}$	$\frac{1}{4}$	$\frac{1}{8}$	$\frac{1}{2}$	$\frac{1}{8}$

Prove the following results:
$\tan^{-1}\frac{1}{4}+\tan^{-1}\frac{2}{9}=\sin^{-1}\frac{1}{\sqrt5}$

Find the value of k in this question, so that the function f is continuous at the indicated point:
$\text{f(x)}=\begin{cases}3\text{x}-8,&\text{if x}\leq5\\2\text{k},&\text{if x}>5\end{cases}$ at x = 5.

Prove the following Exercise:
$\int^{\frac{\pi}{2}}_{0}2\tan^{3}\text{x dx}=1-\log2$