Question
Write a unit vector in the direction of $\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}$.
✓
Answer
Given:$\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}$
$\big|\vec{\text{b}}\big|=\sqrt{2^2+1^2+2^2}$ $=\sqrt{4+1+4}$ $=\sqrt9$ $=3$ $\therefore$ Unit vector $=\frac{\vec{\text{b}}}{\big|\vec{\text{b}}\big|}=\frac{1}3\big(2\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}\big)$ $=\frac{2}3\hat{\text{i}}+\frac{1}3\hat{\text{j}}+\frac{2}3\hat{\text{k}}$
$\big|\vec{\text{b}}\big|=\sqrt{2^2+1^2+2^2}$ $=\sqrt{4+1+4}$ $=\sqrt9$ $=3$ $\therefore$ Unit vector $=\frac{\vec{\text{b}}}{\big|\vec{\text{b}}\big|}=\frac{1}3\big(2\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}\big)$ $=\frac{2}3\hat{\text{i}}+\frac{1}3\hat{\text{j}}+\frac{2}3\hat{\text{k}}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Give alternative arrangement of the switching following circuit, has minimum switches.
Find the general solution of : $\sin \theta=-\frac{\sqrt{3}}{2}$
→Write the value of $\big[\hat{\text{i}}+\hat{\text{j}}\hat{\text{j}}+\hat{\text{k}}\hat{\text{k}}+\hat{\text{i}}\big].$
→If the vectors $3\hat{\text{i}}-2\hat{\text{j}}-4\hat{\text{k}}$ and $18\hat{\text{i}}-12\hat{\text{j}}-\text{m}\hat{\text{k}}$ are parallel, find the value of m.
→Find the principal value of the following:
$\sec^{-1}(2)$
→$\sec^{-1}(2)$
Differentiate the following with respect to x:
$\cos^{-1}(\sin\text{ x})$
→$\cos^{-1}(\sin\text{ x})$
If $\text{A}=\begin{bmatrix}1&2\\3&-1 \end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&-4\\3&-2\end{bmatrix},$ find |AB|.
→In $\triangle ABC$, prove that $( b - c )^2 \cos ^2\left(\frac{ A }{2}\right)+( b + c )^2 \sin ^2\left(\frac{ A }{2}\right)= a ^2$
→Evaluate :
→$\int_0^{\pi / 2} \log \tan x \cdot d x$
Write the principal value of $\sin^{-1}\Big\{\cos\Big(\sin^{-1}\frac{1}{2}\Big)\Big\}$
→