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,7N and 13N respectively

Answer 1

I hope this answer would be helpful for you

Answer 2

Given vectors P= 5N, Q=12N

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

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

$cosA=\frac { 120 }{ 120 } =1 \Rightarrow A= 0\quad {cos0=1}$

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

Then $R=\sqrt { \left( { P }^{ 2 }+{ Q }^{ 2 }+2PQcosA \right) } \Rightarrow 49=169 + 120 cosB$

$cosB=\frac { -120 }{ 120 } =-1 \Rightarrow B=180\quad {cos180 =-1}$

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

Then $R=\sqrt { \left( { P }^{ 2 }+{ Q }^{ 2 }+2PQcosA \right) } \Rightarrow 169=169 + 120 cosC$

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