Question

What is the angle that the given vector makes with y-axis? Ā=2i + √12j​

Answer 1

Topic :-

Vectors

Given :-

$\overrightarrow{A}=2\:\hat{i}+\sqrt{12}\:\hat{j}$

To Find :-

Angle that given vector makes with y-axis.

Concept Used :-

$\overrightarrow{A}=A_x\:\hat{i}+A_y\:\hat{j}$

$A_x=x-component\:of\:\overrightarrow{A}$

$A_y=y-component\:of\:\overrightarrow{A}$

$If \:\theta\:is\:angle\:made\:by\:\overrightarrow{A}\:with\:x-axis\:then:$

$tan\theta=\dfrac{y-component\:of\:\overrightarrow{A}}{x-component\:of\:\overrightarrow{A}}=\dfrac{A_y}{A_x}$

Solution :-

Finding components in given vector,

$On\:comparing\:given\:vector\:with\:\overrightarrow{A}=A_x\:\hat{i}+A_y\:\hat{j},we\:get,$

$y-component\:of\:vector=A_y= \sqrt{12}$

$x-component\:of\:vector=A_x= 2$

Applying formula,

$tan\theta=\dfrac{\sqrt{12}}{2}$

$tan\theta=\dfrac{2\sqrt{3}}{2}$

$tan\theta=\dfrac{\not{2}\sqrt{3}}{\not{2}}=\sqrt{3}$

$tan\theta=tan\:60^{\circ}$

$\theta = 60^{\circ}$

Calculating angle from y-axis,

$Angle\:from\:y-axis=90^{\circ}-\theta$

(It is so because angles formed by a vector from 'x' and 'y' axis are complementary angles.)

$\because \theta = 60^{\circ}$

$Angle\:from\:y-axis=90^{\circ}-60^{\circ}$

$Angle\:from\:y-axis=30^{\circ}$

Answer :-

The given vector makes $\bold {30^{\circ}}$ with y-axis.

Answer 2

QuestioN :

What is the angle that the given vector makes with y-axis? Ā=2i + √12j

GiveN :

• Ā=2i + √12j

To FiNd :

• The angle between A and y-axis

ANswer :

The angle between A and y-axis is 30°.

SolutioN :

$\sf tan0 = \frac{\sqrt{12} }{2}$

$\sf tan0 = \frac{2\:\sqrt{3} }{2}$

$\sf tan0= \sqrt{3}$

$\sf tan0 = tan60$

$\sf 0 = 60$

$\sf Angle\: Y = 90$

$\sf By\: using\: formula=90-60$

$\sf Y-axis = 30$