Question

The points with position vectors , $40 \hat { i } - 8 \hat { j }$ and are collinear if

• A. a = - 40
• B. a = 40
• C. a = 20
• D. None of these

Answer 1

Answer: (A)

a = - 40

Answer 2

The points are collinear

⇒ λ() + μ( $40 \hat { i } - 8 \hat { j }$ ) + ν( $a \hat { i } - 52 \hat { j }$ ) = 0 with

λ +μ + ν = 0

⇒ 60 λ + 40μ + νa = 0,

3 λ – 8μ – 52ν = 0,

λ + μ + ν = 0.

For non-zero set (λ, μ, ν) , = 0

⇒ a = – 40