Download App

VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA2 Marks
Question
For given vectors, $\vec{a}=2\hat{i}-\hat{j}+2\hat{k}\ \ \text{and}\ \vec{b}=-\hat{i}+\hat{j}-\hat{k},$ find the unit vector in the direction of the vector $\vec{a}+\vec{b}.$
✓

Answer

The given vectors are $\vec{a}=2\hat{i}-\hat{j}+2\hat{k}\ \ \text{and}\ \vec{b}=-\hat{i}+\hat{j}-\hat{k}$

$\vec{a}=2\hat{i}-\hat{j}+2\hat{k}$

$\vec{b}=-\hat{i}+\hat{j}-\hat{k}$

$\therefore\vec{a}+\vec{b}=(2-1)\hat{i}+(-1+1)\hat{j}+(2-1)\hat{k}$ $=1\hat{i}+0\hat{j}+1\hat{k}=\hat{i}+\hat{k}$

$\big|\vec{a}+\vec{b}\big|=\sqrt{1^2+1^2}=\sqrt{2}$

Hence, the unit vector in the direction of $\big(\vec{a}+\vec{b}\big)$ is

$\frac{\big(\vec{a}+\vec{b}\big)}{\big|\vec{a}+\vec{b}\big|}=\frac{\hat{i}+\hat{k}}{\sqrt{2}}=\frac{1}{\sqrt{2}}\hat{i}+\frac{1}{\sqrt{2}}\hat{k}$

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" 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

Let A = [aij] be a square matrix of order 3 × 3 and Cij denote cofactor of aij in A. if |A| = 5, write the value of a13C13 + a23C23 + a33C33.
→
Find the value of y, if $\begin{bmatrix}\text{x}-\text{y}&2\\\text{x}&5 \end{bmatrix}=\begin{bmatrix}2&2\\3&5 \end{bmatrix}$
→
Show that $\left( {\vec a - \vec b} \right) \times \left( {\vec a + \vec b} \right) = 2\left( {\vec a \times \vec b} \right)$
→
Write the principal value of $\sin^{-1}\Big\{\cos\Big(\sin^{-1}\frac{1}{2}\Big)\Big\}$
→
Evaluate the following:
$\sin\Big(\frac{1}{2}\cos^{-1}\frac{4}{5}\Big)$
→
Find the value of x, if:
$\begin{vmatrix}2&4\\5&1\end{vmatrix}=\begin{vmatrix}2\text{x}&4\\6&\text{x}\end{vmatrix}$
→
Show that the function f defined by f(x) = |1 – x + | x | |, where x is any real number, is a continuous function.
→
A bag contains 4 white balls and 2 black balls. Another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that,
Both are white.
→
Differentiate w.r.t. x, the function, log7 (log x)
→
Let C denote the set of all complex numbers. A function f : C → C is defined by f(x) = x3. Write f-1(1).
→