Let x^2 + y^2 = 1; u^2 + v^2 = 1 and xu + yv = 0, then 1. x^2 + u^2 = 1 2. y^2 + v^2 = 1 3. xu + yv = 0 Which of the above is/are true?

CAPF AC 2019 PYQ with Answer — Let x^2 + y^2 = 1; u^2 + v^2 = 1 and xu + yv = 0, then 1. x^2 + u^2 =…

2019 · Q42

Let x^2 + y^2 = 1; u^2 + v^2 = 1 and xu + yv = 0, then

1x^2 + u^2 = 1
2y^2 + v^2 = 1
3xu + yv = 0

Which of the above is/are true?

general-mental-abilityquantitative-aptitude

A3 only
B1 and 2 only
C1, 2 and 3
D2 and 3 only

Explanation

(x,y) and (u,v) are unit vectors with zero dot product - i.e. orthonormal. From xu = -yv, squaring and substituting x^2 = 1-y^2 and u^2 = 1-v^2 gives y^2 + v^2 = 1 (statement 2 true), and likewise x^2 + u^2 = 1 (statement 1 true); statement 3 is given. Hence 1, 2 and 3 - C.