Find a vector of magnitude 4 units which is parallel to the vecto… - Vidyadip

Question

Find a vector of magnitude 4 units which is parallel to the vector $\sqrt3\hat{\text{i}}+\hat{\text{j}}$.

✓

Answer

Let $\vec{\text{a}}=\sqrt3\hat{\text{i}}+\hat{\text{j}}$
Then, $\big|\vec{\text{a}}\big|=\sqrt{\big(\sqrt3\big)^2+1}=\sqrt{3+1}=\sqrt4=2$
A unit vector parallel to $\vec{\text{a}}=\hat{\text{a}}=\frac{\vec{\text{a}}}{|\vec{\text{a}}|}=\frac{1}2\big(\sqrt3\hat{\text{i}}+\hat{\text{j}}\big)$
Hence, Required vector $=4\hat{\text{a}}=4\times\frac{1}2\big(\sqrt3\hat{\text{i}}+\hat{\text{j}}\big)=2\sqrt3\hat{\text{i}}+2\hat{\text{j}}$

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" from Algebra of Vectors→Algebra of Vectors — 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 the determinant $\left|\begin{array}{cc}x^2-x+1 & x-1 \\ x+1 & x-1\end{array}\right|$.

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that.
One of them is black and other is red.

Evaluate the following integrals:
$\int\bigg (2^{\text{x}}+\frac{5}{\text{x}}-\frac{1}{\text{x}^{\frac{1}{3}}}\bigg)\text{dx}$

Find the magnitude of two vectors $\vec{a}\ \text{and}\ \vec{b},$ having the same magnitude and such that the angle between them is 60° and their scalar product is $\frac{1}{2}\cdot$

A matrix X has a + b rows and a + 2 columns while the matrix Y has b + 1 rows and a + 3 columns. Both matrices XY and YX exist. Find a and b. Can you say XY and YX are of the same type? Are they equal.

If either vector $\vec{a}=\vec{0}$ or $\vec{b}=\vec{0}$, then $\vec{a} \cdot \vec{b}$ = 0. But the converse need not be true. Justify your answer with an example.

If A = {2, 3, 4}, B = {1, 3, 7} and R = {(x, y): x ∈ A, y ∈ B and x < y} is a relation from A to B, then write R^-1.

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

Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have same number of pages} is an equivalence relation.

Find $x$ and $y$, if $2\left[\begin{array}{ll}1 & 3 \\ 0 & x\end{array}\right]+\left[\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right]=\left[\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right]$.