MHT CET202613 April 2026Evening ShiftPhysicsMathematics in PhysicsActual
Calculate the values of a and b if vectors a i + b j = n and ( i + j ) are perpendicular to each other
Options
- A1 2 , 1 2
- B0, 0
- C2 , - 1 2
- D( 1 2 ), (- 1 2 )
Correct answer
D. ( 1 2 ), (- 1 2 )
Step-by-step solution
Given v ₁ = a i + b j = n and v ₂ = i + j . Since v ₁ is a unit vector, its magnitude is 1 . a^2 + b^2 = 1 Since v ₁ and v ₂ are perpendicular, their dot product is zero. (a i + b j ) ( i + j ) = 0 a + b = 0 b = -a Substituting b = -a in the magnitude equation: a^2 + (-a)^2 = 1 2a^2 = 1 a = 1 2 For a = 1 2 , b = - 1 2 . Answer: ( 1 2 ), (- 1 2 )