Which of the following is not a unit vector f | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) vector $\vec{v} = x\,i + y\,j$ is a unit vector if its magnitude $|\vec{v}| = \sqrt{x^2 + y^2} = 1$,which implies $x^2 + y^2 = 1$.For option $A$:

Vedclass · Accepted Answer

$(\sin 2	heta )\,i - (\cos 	heta )\,j$

Vedclass · Answer

(C) vector $\vec{v} = x\,i + y\,j$ is a unit vector if its magnitude $|\vec{v}| = \sqrt{x^2 + y^2} = 1$,which implies $x^2 + y^2 = 1$.For option $A$: $(\cos 	heta)^2 + (-\sin 	heta)^2 = \cos^2 	heta + \sin^2 	heta = 1$.For option $B$: $(\sin 	heta)^2 + (\cos 	heta)^2 = \sin^2 	heta + \cos^2 	heta = 1$.For option $C$: $(\sin 2	heta)^2 + (-\cos 	heta)^2 = \sin^2 2	heta + \cos^2 	heta$. This is not equal to $1$ for all values of $	heta$ (e.g.,at $	heta = \frac{\pi}{4}$,$\sin^2(\frac{\pi}{2}) + \cos^2(\frac{\pi}{4}) = 1^2 + (\frac{1}{\sqrt{2}})^2 = 1 + 0.5 = 1.5 
eq 1$).For option $D$: $(\cos 2	heta)^2 + (-\sin 2	heta)^2 = \cos^2 2	heta + \sin^2 2	heta = 1$.Therefore,the vector in option $C$ is not a unit vector for all values of $	heta$.

Which of the following is not a unit vector for all values of $\theta$?

Similar Questions

The number of values of $m \in R$ for which the vectors $\hat{i}+2 \hat{j}+m \hat{k}$ and $\hat{i}+m \hat{j}+2 \hat{k}$ are collinear is

If the sides of a regular hexagon $ABCDEF$ are given by $\vec{AB} = \bar{a}$ and $\vec{BC} = \bar{b}$,then $\vec{FA} = .....$

The points in space represented by the position vectors $A = 4\hat{i}+\hat{j}+3\hat{k}$,$B = 6\hat{i}-2\hat{j}-3\hat{k}$,and $C = \hat{i}-\hat{j}-3\hat{k}$ form:

The projection of the vector $i+j+k$ along the vector $j$ is

If $\bar{a}, \bar{b}, \bar{c}$ are three unit vectors such that $|\bar{a}+\bar{b}|^2+|\bar{a}+\bar{c}|^2=8$,then $|\bar{a}+3\bar{b}|^2+|\bar{a}+3\bar{c}|^2=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module