If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the point (7, 17) and (15, β), then β equals :

Engineering

Mathematics

Angle Between two Lines

Question

– 5

$\frac{35}{3}$

$\frac{- 35}{3}$

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Line perpendicular to 2x – 3y + 5 = 0 is 3x + 2y + c = 0

Which is satisfied by point (7, 17)

⇒ 3(7) + 2(17) + c = 0

⇒ c =– 55

⇒ equation of line is 3x + 2y – 55 = 0

⇒ 3(15) + 2(β)– 55 = 0

⇒ 2β = 55 – 45 ⇒ β = 5