Verified Solution • 2025–26 Session moderate

QJEEM21Mac6b4: JEE Main 2021 Physics - Class 11 JEEM21Mac6b4 Solution: A vector has components 3p and 1 with respect to a rectangular…

A vector a→\overrightarrow 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→\overrightarrow a has components p + 1 and 10\sqrt {10} , then the value of p is equal to :

Multiple Choice Options

  • A 1
  • B −54- {5 \over 4}
  • C 45{4 \over 5}
  • D −- 1

Step-by-Step Verified Solution

∣a→∣old=∣a→∣new{\left| {\overrightarrow a } \right|_{old}} = {\left| {\overrightarrow a } \right|_{new}}

(3p)2 + 1 = (p + 1)2 + 10

⇒\Rightarrow 9p2 −- p2 −- 2p −- 10 = 0

⇒\Rightarrow 8p2 −- 2p −- 10 = 0

⇒\Rightarrow 4p2 −- p −- 5 = 0

⇒\Rightarrow 4p2 −- 5p + 4p −- 5 = 0

⇒\Rightarrow (4p −- 5) (p + 1) = 0

⇒\Rightarrow p = 54{5 \over 4} , −- 1

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