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Question: Answered & Verified by Expert
A vector a has components \( 3 p \) 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 \( \sqrt{10} \), then a value of \( p \) is equal to:
MathematicsVector AlgebraJEE Main
Options:
  • A \( 1 \)
  • B \( -\frac{5}{4} \)
  • C \( \frac{4}{5} \)
  • D \( -1 \)
Solution:
1977 Upvotes Verified Answer
The correct answer is: \( -1 \)

aOld=3pi^+j^

aNew=(p+1)i^+10j^

aOld=aNew

ap2+1=p2+2p+1+10

8p2-2p-10=0

4p2-p-5=0

(4p-5)(p+1)=0p=54,-1

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