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The resultant of two vectors P and Q is R . When the direction of Q is reversed, the resultant is given by S . Which one of the following is true for vectors R and S ?

Options

  1. AR ²- S ²= ( P ²+ Q ² )
  2. BR ²- S ²=2( P Q )
  3. CR ²+ S ²=4( P Q )
  4. DR ²+ S ²=2 ( P ²+ Q ² )

Correct answer

D. R ²+ S ²=2 ( P ²+ Q ² )

Step-by-step solution

(B) Given, P+Q=R After reversing direction of R , we gel array l r=-P-Q S=-P-Q array So let angle between P and Q be Q So resurtants. array l R²=p²+Q²+2 P Q ...(1) s²=p²+Q²-2 P Q ...(2) array Adthing equation (1) and (2) R²+S²=2 (P²+Q² ) So, the corvect answer is R²+s²=2 (p²+Q² )

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