Question

Q.4
A vector a has components 2p & 1 with respect to a rectangular cartesian system The system is rotated
through a certain angle about the origin in the counterclockwise sense If with respect to the new system a
has components p+1 & 1 then
(A)p=0
(B) p=1 or p=-1/3
(Cp=-1 of p=1/3
(D) p=1 of p =-1​

Answer 1

Let i,j be unit vectors along the co-ordinate axes 

∴a=2pi+1.j    ....(1)

On rotation, let b be the vector having components p+1 and 1.

∴b=(p+1)i+1.j   ...(2)

where i,j are units vectors along the new co-ordinate axes.

But on rotation magnitude of the initial and final vector will remain same

∣∣∣∣b∣∣∣∣=∣a∣⇒∣b∣2=∣a∣2

⇒(p+1)2+1=(2p)2+1⇒3p2−2p−1=0

⇒(3p+1)(p−1)=0⇒p=1 or p=−31

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Answer 2

Answer:

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