Question

Answer this Question of iit jee . Chapter → Three dimensional Geometry​

Answer 1

EXPLANATION.

The two lines.

⇒ x = ay + b, z = cy + d.

⇒ x = a'y + b', z = c'y + d'.

Are perpendicular to each other.

As we know that,

We can write equation as,

⇒ (x - b)/a = y/1 = (z - d)/c.

⇒ (x - b')/a' = y/1 = (z - d')/c'.

⇒ a₁ = a, b₁ = 1, c₁ = c.

⇒ a₂ = a', b₂ = 1, c₂ = c'.

Two Lines are perpendicular if,

⇒ a₁ a₂ + b₁ b₂ + c₁ c₂ = 0.

⇒ (a)(a') + (1)(1) + (c)(c') = 0.

⇒ aa' + 1 + cc' = 0.

⇒ aa' + cc' = - 1.

Option [A] is correct answer.

Answer 2

Answer:

option (a) aa' + cc' +1 = 0

Step-by-step explanation:

Given :- Two lines x = ay + b , z = cy + d

and x = a'y + b' , z = c'y + d'

Given equation x = ay+ b , z = cy + d can be Rewritten as

x - b / a = y - 0 / 1 = z - d / c

• , x - b / a = y - 0 / 1 = z -d / c

and , x = a'y + b' , z = c'y + d can be Rewritten as

• x - b' / a' = y - 0 / 1 = z - d' / c'

these points will be perpendicular if a(a' + cc' + 1 = 0 [∵ l₁l₂ + m₁m₂ + n₁n₂ = 0]