Question

If P + Q = P - Q and theta is the angle between P and Q then A. Theta =0degree B. Theta = 90degree C. P=0 D. Q= 0

Answer 1

The correct answer for this question is option (B) Theta = 90

Explanation :

• Since the given vectors are P and Q .

• Also it is given that the angle between the vectors P and Q is = $\theta$
• ∴|P+Q| =$\sqrt{P^2 + Q^2 + 2PQcos \theta }$
• Also |P - Q | = $\sqrt{P^2 + Q^2 - 2PQcos \theta }$
• Since , it is given that |P+Q| = |P-Q| , so we have :

     $\sqrt{P^2 + Q^2 + 2PQcos \theta } = \sqrt{P^2 + Q^2 -2PQcos \theta }$

   Or , $P^2 + Q^2 + 2PQcos \theta } = P^2 + Q^2 -2PQcos \theta }$

   Or , $2PQcos \theta +2 PQ cos \theta = 0$

   Or , 4PQcos$\theta$ = 0

   Or , $cos \theta = 0$

    So , $\theta$  = 90

Hence , for the given condition , $\theta$  = 90 degree is correct .

Answer 2

Answer:

option b) and d) both are correct.

Explanation:

Why I chose option d):

iP+Q= P-Q                    (vectors)

now, if Q=0

then it will become null vector, therefore no direction and no quantity, only a quantity formed by cancellation of two vectors.

P+Q = P-Q can be written as P=P     (vectors), which is correct.

Why I chose option b):

⇒P+Q=P-Q

⇒P²+Q²+2PQcosФ=P²+Q²-2PQcosФ

⇒4PQcosФ=0

⇒cosФ=0

⇒Ф=90°