MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Distance between Two Parallel Planes

If two lines ...

Question

If two lines joining the pair of points $(4, 1, 2)$ , $(p, 3, 0)$ , $(2, 1, - 1)$ , and $(4, 3, 2)$ are mutually perpendicular to each other then find the value of $p$ .

Open in App

Solution

$\begin{matrix} A (4, 1, 2), B (p, 3, 0) L i n e j o i n i n g A a n d B i s p a r a l l e l t o 4 - p, 1 - 3, 2 - 0 (4 - p, - 2, 2) C (2, 1, - 1) D (4, 3, 2) L i n e j o i n i n g C a n d D i s p a r a l l e l t o 2 - 4, 1 - 3, - 1 - 2 (- 2, - 2, - 3) - 2 (4 - p) - 2 (- 2) + 2 (- 3) = 0 - 8 + 2 p + 4 - 6 = 0 2 p = 0 p = 5 \end{matrix}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. If the lines joining the points

(K, 2), (3, 6)

(2, 3), (K, 7)

are perpendicular to each other, then the possible value of

K

Q. Find the equation of the line passing through the point (1, −1, 1) and perpendicular to the lines joining the points (4, 3, 2), (1, −1, 0) and (1, 2, −1), (2, 1, 1).

p_{1}, p_{2}

are the perpendicular distances from the origin to the two straight lines which are perpendicular to each other, then the locus of the point of intersection of the perpendicular lines is

Q. Find the value of

k

, if the lines joining to the points of inter section of the curve

2 x^{2} - 2 x y + 3 y^{2} + 2 x - y - 1 = 0

x + 2 y = k

are mutually perpendicular.

Q. If the lines

(p + 1) x + y = 3

3 y - (p - 1) x = 4

are perpendicular to each other, find

p

.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Drawing Tangents to a Circle

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Distance between Two Parallel Planes

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon