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.

Rate this question :

Find the value of λ so that the lines

and are perpendicular to each other.

Mathematics - Board PapersShow that lines and intersect. Also find their point of intersection.

Mathematics - Board PapersFind the value of so that the following lines are perpendicular to each other.

Mathematics - Board Papers

Find the value of λ so that the lines and are perpendicular to each other.

Mathematics - Board PapersWrite the direction cosines of the vector

Mathematics - Board PapersFind the angle between the lines 2x = 3y = –z and 6x = –y = –4z.

RD Sharma - Volume 2Find the value of λ, so that the lines and are at right angles. Also, find whether the lines are intersecting or not.

Mathematics - Board PapersIf and respectively are the position vectors of points A, B, C and D, then find the angle between the straight lines and . Find whether and are collinear or not.

Mathematics - Board PapersWrite the angle between the lines and

RD Sharma - Volume 2