Question

The resultant of two vector A & B is
C. If direction of B is reversed the
resultant is D. Then which of the
following is true?
(A) C2 + D2 = A² + B2
(B) A2 + C2 = B2 + D2
(C) C2 + D2 = 2(A? + B2)
(
DC2-D2 = A + B2​

Answer 1

Explanation:

the correct answer is c

Answer 2

Answer:

C^2+D^2=2(A^2+B^2)

Explanation:

A vector + B vector = D vector

then D^2 = A^2 + B^2 + 2cos teta    ------ equation 1

A vector - B vector = C vector

then  C^2 = A^2 + B^2 - 2cos teta    ------equaton 2

while adding equation 1 and 2

C^2+D^2= A^2 + B^2 + 2cos teta + A^2 + B^2 - 2cos teta

cancelling     + 2cos teta and  - 2cos teta

then C^2+D^2= A^2 + B^2 + A^2 + B^2

C^2+D^2 = 2A^2 + 2B^2

C^2+D^2 = 2 ( A^2 + B^2 )  

therefore the answer is option C