Home
Class 12
MATHS
Let P(3,2,6) be a point in space and Q b...

Let `P(3,2,6)` be a point in space and `Q` be a point on line ` vec r=( hat i- hat j+2 hat k)+mu(-3 hat i+ hat j+5 hat k)dot` Then the value of `mu` for which the vector ` vec P Q` is parallel to the plane `x-4y+3z=1` is

A

`(1)/(4)`

B

`-(1)/(4)`

C

`(1)/(8)`

D

`-(1)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
A
Any point on the line is `Q(-3mu+1,mu-1,5mu+2)`
`PQ=hat(i)(2-3mu)+hat(j)(mu-3)+hat(k)(5mu-4)`
Since, PQ is parallel to x-4y+3z=1 therefore normal line is perpendicular to the line.
`rArr" "1(2-3mu)-4(mu-3)+3(5mu-4)=0`
`rArr" "mu=(1)/(4)`
Promotional Banner

Topper's Solved these Questions

  • PLANE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Practice exercise (Exercise 1) Topical problems (Angle between the planes and angle between line and plane)|13 Videos

  • PLANE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Practice exercise (Exercise 1) Topical problems (Coplanarity of two lines and distance of a point from a plane)|16 Videos

  • PAIR OR STRAIGHT LINES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|13 Videos

  • PRACTICE SET 01

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

Similar Questions

Explore conceptually related problems

Let P(3,2,6) be a point in space and Q be a point on line vec r=(hat i-hat j+2hat k)+mu(-3hat i+hat j+5hat k) Then the value of mu for which the vector vec PQ is parallel to the plane x-4y+3z=1 is a.1/4 b.-1/4 c.1/8d. -1/8

A point on the line vec r=2hat i+3hat j+4hat k+t(hat i+hat j+hat k) is

vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

Vectors vec A=hat i+hat j-2hat k and vec B=3hat i+3hat j-6hat k are

The lines vec r=(hat i+hat j+hat k)alpha+3hat k and vec r=(hat i-2hat j+hat k)beta+3hat k

If vec r=x hat i+y hat j+z hat k ,\ then write the value of | vec rxx hat i|^2dot

Vector equation of the plane r=hat i-hat j+lambda(hat i+hat j+hat k)+mu(hat i2hat j+3hat k) in the scalar dot product form is

Consider a line vec r=hat i+t(hat i+hat j+hat k) and a plane (vec r-(hat i+hat j))*(hat i-hat j-hat k)=1

If line vec r=( hat i-2 hat j- hat k)+lambda(2 hat i+ hat j+2 hat k) is parallel to the plane vec r.(3 hat i-m hat k)=14 , then the value of m is (1). 2 (2) -2 (3) 0 (4) 3

If vec a= hat i+ hat j+ hat k , vec b=2 hat i- hat j+3 hat k a n d vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec cdot