JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Vector Algebra

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

10

, then a value of

p

is equal to :

(A)-1✓ Correct
(B) $\frac{4}{5}$
(C) $- \frac{5}{4}$
(D)1

Answer: (A)

Solution

Rotating the axes changes the components but not the length of

a

, so

(3 p)^{2} + 1^{2} = (p + 1)^{2} + (10)^{2}

That is

9 p^{2} + 1 = p^{2} + 2 p + 11

, so

8 p^{2} - 2 p - 10 = 0

and

4 p^{2} - p - 5 = 0

. Factoring,

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

, so the two roots are

p = \frac{5}{4}

and

p = - 1

, and a value of

p

- 1

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Single correct option

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