Q. 64.1( 19 Votes )

# If the lines <spa

Answer :

Two lines and

are perpendicular to each other if

a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2} = 0

Given -

comparing with

we get -

x_{1} =1, y_{1} = 2, z_{1} = 3

& a_{1} = - 3, b_{1} = 2k, c_{1} = 2

Similarly,

comparing with

we get -

x_{2} = 1, y_{2} = 2, z_{2} = 3

& a_{2} = 3k, b_{2} = 1, c_{2} = -5

Since the two lines are perpendicular,

a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2} = 0

⇒ (-3) × 3k + 2k × 1 + 2 × (-5) = 0

⇒ -9k + 2k - 10 = 0

⇒ -7k = 10

∴ k = -10/7

Hence, the value of k is -10/7.

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