Two forces $$\left( {\overrightarrow P + \overrightarrow Q } \right)$$ and $$\left( {\overrightarrow P - \overrightarrow Q } \right)$$ where $$\overrightarrow P \bot \overrightarrow Q $$, when act at an angle $$\theta$$1 to each other, the magnitude of their resultant is $$\sqrt {3({P^2} + {Q^2})} $$, when they act at an angle $$\theta$$2, the magnitude of their resultant becomes $$\sqrt {2({P^2} + {Q^2})} $$. This is possible only when $${\theta _1} < {\theta _2}$$.
Statement II :
In the situation given above.
$$\theta$$1 = 60$$^\circ$$ and $$\theta$$2 = 90$$^\circ$$
In the light of the above statements, choose the most appropriate answer from the options given below :-
A
Statement I is false but Statement II is true
B
Both Statement I and Statement II are true
C
Statement I is true but Statement II is false
D
Both Statement I and Statement II are false.
Explanation
$$\overrightarrow A = \overrightarrow P + \overrightarrow Q $$
$$\overrightarrow B = \overrightarrow P - \overrightarrow Q $$
For $$\left| {\overrightarrow A + \overrightarrow B } \right| = \sqrt {3({P^2} + {Q^2})} $$
$${\theta _1} = 60^\circ $$
For $$\left| {\overrightarrow A + \overrightarrow B } \right| = \sqrt {2({P^2} + {Q^2})} $$
$${\theta _2} = 90^\circ $$
2
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
The resultant of these forces $$\overrightarrow {OP} ,\overrightarrow {OQ} ,\overrightarrow {OR} ,\overrightarrow {OS} $$ and $$\overrightarrow {OT} $$ is approximately .......... N.
[Take $$\sqrt 3 = 1.7$$, $$\sqrt 2 = 1.4$$ Given $$\widehat i$$ and $$\widehat j$$ unit vectors along x, y axis]
The magnitude of vectors $$\overrightarrow {OA} $$, $$\overrightarrow {OB} $$ and $$\overrightarrow {OC} $$ in the given figure are equal. The direction of $$\overrightarrow {OA} $$ + $$\overrightarrow {OB} $$ $$-$$ $$\overrightarrow {OC} $$ with x-axis will be :
