Question

There are two force vectors, one of $5N$ and other of $12N$ at what angle the two vectors be added to get resultant vector of $17N$ and $13N$ respectively.

• A. $0^{\circ },{180}^{\circ }and{90}^{\circ }$
• B. $0^{\circ },{90}^{\circ }and{180}^{\circ }$
• C. $0^{\circ },{90}^{\circ }and{90}^{\circ }$
• D. ${180}^{\circ },0^{\circ }and{90}^{\circ }$

Answer 1

The correct option is A $0^{\circ },{180}^{\circ }and{90}^{\circ }$

Given vectors $P=5N,Q=12N$

Case 1: When resultant$R=17N$; let us assume angle between vectors is A

Then $R=\sqrt{P^2+Q^2+2PQcosA}=289\Rightarrow 169+120cosA$

$cosA=\frac{120}{120}\Rightarrow A=0$

Case 2: when resultant R =7N; let us assume angle between vectors is B

Then , $R=\sqrt{P^2+Q^2+2PQcosB}=49\Rightarrow 169+120cosB$

$cosB=\frac{-120}{120}\Rightarrow B={180}^0$

Case 3: when resultant R =13N; let us assume angle between vectors is C

Then , $R=\sqrt{P^2+Q^2+2PQcosC}=169\Rightarrow 169+120cosC$

$cosC=\frac{0}{120}\Rightarrow C={90}^0$