Find the values of p so the line and

are at right angles.

Open in App

Solution

The given equations can be written in the standard form as

and

The direction ratios of the lines are −3,, 2 and respectively.

Two lines with direction ratios, a₁, b₁, c₁ and a₂, b₂, c₂, are perpendicular to each other, if a₁a₂ + b₁ b₂ + c₁c₂ = 0

Thus, the value of p is .

Suggest Corrections

Similar questions

Q. Find the values of p so the line and are at right angles.

Q. Find the values of

p

so the line

\frac{1 - x}{3} = \frac{7 y - 14}{2 p} = \frac{z - 3}{2}

and

\frac{7 - 7 x}{3 p} = \frac{y - 5}{1} = \frac{6 - z}{5}

are at right angles.

Find the value of p so that the lines $\frac{1 - x}{3} = \frac{7 y - 14}{2 p} = \frac{z - 3}{2} a n d \frac{7 - 7 x}{3 p} = \frac{y - 5}{1} = \frac{6 - z}{5}$ are at right angles

Q. Find the values of

p

so that the line

1 - x

\frac{1 - x}{3} = \frac{7 y - 14}{2 p} = \frac{z - 3}{2}

and

\frac{7 - 7 x}{3 p} = \frac{y - 5}{1} = \frac{6 - z}{5}

are at right angles.

Q. Find the value of

λ,

so that the lines

\frac{1 - x}{3} = \frac{7 y - 14}{λ} = \frac{z - 3}{2} and \frac{7 - 7 x}{3 λ} = \frac{y - 5}{1} = \frac{6 - z}{5}

are at right angles. Also, find whether the lines are intersecting or not.

Join BYJU'S Learning Program

Find the values of p so the line and are at right angles.

The given equations can be written in the standard form as and The direction ratios of the lines are −3,, 2 and respectively. Two lines with direction ratios, a1, b1, c1 and a2, b2, c2, are perpendicular to each other, if a1a2 + b1 b2 + c1c2 = 0 Thus, the value of p is .

Find the values of p so the line and

are at right angles.