1. Tardigrade
  2. Question
  3. Mathematics
  4. A vector veca 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, veca has components p+1 and √10, then a value of p is equal to:

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A vector $\vec{a}$ 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, $\vec{a}$ has components $p+1$ and $\sqrt{10}$, then a value of p is equal to:

JEE MainJEE Main 2021Vector Algebra

Solution:

$\overrightarrow{a}_{\text {Old }}=3 p \hat{i}+\hat{j} $
$\overrightarrow{a}_{\text {New }}=(p+1) \hat{i}+\sqrt{10} \hat{j} $
$\Rightarrow\left|\overrightarrow{a}_{Old}\right|=\left|\overrightarrow{a}_{\text {New }}\right| $
image
$\Rightarrow ap^2+1=p^2+2 p+1+10 $
$8 p^2-2 p-10=0 $
$4 p^2-p-5=0$
$(4 p -5)( p +1)=0 \rightarrow p =\frac{5}{4},-1$