A vector a → has components 3 p and 1 with respect to a rectangular cartesian system. This system is…

A vector a→ has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, a→ has components p+1 and 10, then a value of p is equal to:
  1. 1
  2. -54
  3. 45
  4. -1

Solution

a→Old=3pi^+j^

a→New=(p+1)i^+10j^

⇒a→Old=a→New

⇒9p2+1=p2+2p+1+10

8p2-2p-10=0

4p2-p-5=0

(4p-5)(p+1)=0⇒p=54,-1

Asked in: JEE Main 2021 (18 Mar Shift 1)

Practice more Vectors questions on Aicharya