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If the lines (1 -x )/(3) = ( 7y - 14)/(2...

If the lines `(1 -x )/(3) = ( 7y - 14)/(2 lamda) = (z - 3)/(2) "and" (7 - 7x)/(3lamda) = (y - 5)/(1) = ( 6 - z ) /(5)` are at right angle, then the value of `lamda` is

A

`70/11`

B

`10/11`

C

`-70/11`

D

`-10/11`

Text Solution

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The correct Answer is:
A
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Find the value of 'lambda' so the lines: (1-x)/(3) = (7y -14)/(lambda) = (z-3)/(2) and (7 - 7x)/(3 lambda) = (y -5)/(1 ) = (6 - z)/(5) are at right angles. Also, find whether the lines are ntersecting or not .

Fiind m, if the lines (1-x)/(3)= ( 7y-14)/(2m ) = (z-3) /(2) and ( 7-7x)/(3m) = (y-5)/(1) = (6-z)/(5) are at right angles.

(i) Find the value of 'p' so that the lines : l_(1) : (1 - x)/(3) = (7y -14)/(2p) = (z - 3)/(2) and l_(2) : (7 -7x)/(3p) = (y - 5)/(1) = (6 - z)/(5) are at right angles. Also, find the equations of the line passing through (3,2, -4) and parallel to line l_(1) . (ii) Find 'k' so that the lines : (x - 3)/(2) = (y + 1)/(3 ) = (z - 2)/(2k) and (x + 2)/(1) = (4 -y)/(k) = (z + 5)/(1) are perpendicular to each other.

Find the value of so that the lines l1: (1-x)/3 = (7y-14)/(2lambda) =(z-3)/2 and l2: (7-7x)/(3lambda) = (y-5)/1 = (6-z)/5 are at right angle. Also find the equation of a line passing through the point (3,2,-4) and parallel to l1.

Find the values p so that line (1-x)/(3)=(7y-14)/(2p)=(z-3)/(2) and (7-7x)/(3p)=(y-5)/(1)=(6-z)/(5) are at right angles.

If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(-2) and (x-1)/(3k)=(y-5)/(1)=(z-6)/(-5) are at right angle,then find the value of k

Find the values of p so that the lines (1-x)/(3)=(7y-14)/(2p)=(z-3)/(2)(7-7x)/(3p)=(y-5)/(1)=(6-z)/(5) are at right angles.

Find the value of so that the lines (-(x-1))/(3)=(7(y-2))/(2lamda)=(z-3)/(2)and(-7(x-1))/(3lamda)=(y-5)/(1)=(-(z-6))/(5) are perpendicular to each other.

If the lines (x-2)/(1)=(y-3)/(1)=(z-4)/(lamda) and (x-1)/(lamda)=(y-4)/(2)=(z-5)/(1) intersect then

Find the values of lambda if the following of lines perpendicular : (1-x)/(3) = (7y-14)/(3lambda)=(z+1)/(2) and (7-7x)/(3lambda) = y/1 = (1-z)/(5)

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