Find the value of m for which thestraigh...

Find the value of `m` for which thestraight line `3x-2y+z+3=0=4x=3y+4z+1` is parallel to the plane `2x-y+m z-2=0.`

-2

-18

Text Solution

Verified by Experts

The correct Answer is:

Vector `((3hati-2hatj+hatk)xx(4hati-3hatj+4hatk))` is perpendicular to `2hati-hatj+mhatk`. Thus,
`|[3,-2,1],[4,-3,4],[2,-1,m]|=0orm=-2`

Topper's Solved these Questions

THREE-DIMENSIONAL GEOMETRY
CENGAGE|Exercise Exercise (Multiple)|17 Videos
THREE-DIMENSIONAL GEOMETRY
CENGAGE|Exercise Exercise (Reasoning Questions)|10 Videos
THREE-DIMENSIONAL GEOMETRY
CENGAGE|Exercise SUBJECTIVE TYPE|1 Videos
THREE DIMENSIONAL GEOMETRY
CENGAGE|Exercise Question Bank|12 Videos
TRIGNOMETRIC RATIOS IDENTITIES AND TRIGNOMETRIC EQUATIONS
CENGAGE|Exercise Question Bank|4 Videos

Similar Questions

Explore conceptually related problems

The value of m for which straight lein 3x-2y+z+3=0=4 x-3y+4z+1 is parallel to the plane 2x-y+m z-2=0 is a. -2 b. 8 c. -18 d. 11

Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z-4 and is parallel to the line of intersection of the planes 2x + 3y +z=1 and x + 3y + 2z = 2 be x + Ay + Bz + C=0 Compute the value of |A+B+C| .

Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0

Find the distance of the point P(3,8,2) from the line 1/2(x-1)=1/4(y-3)=1/3(z-2) measured parallel to the plane 3x+2y-2z+15=0.

Find the image of the line (x-1)/2=(y+1)/(-1)=(z-3)/4 in the plane 3x-3y+10 z-26=0.

Equation of the plane containing the straight line x/2=y/3=z/4 and perpendicular to the plane containing the straight lines x/2=y/4=z/2 and x/4=y/2=z/3 is

Equation of line passing through A(1,0,3), intersecting the line (x/2=(y-1)/3=(z-2)/1) and parallel to the plane x+y+z=2 is

Find the equation of the plane passing through the intersection of the planes vecr*(2hati+3hatj)=1 and 3x-4y+3z=8 and is perpendicular to the plane x+2y-z+6=0 .

Find the Vector and Cartesian equation of the plane containing the line (x-2)/2=(y-2)/3=(z-1)/3 and parallel to the line (x+1)/3=(y-1)/2=(z+1)/1

CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)

Let L1 be the line vec r1=2 hat i+ hat j- hat k+lambda(i+1 hat k) and...
Text Solution
|
For the line (x-1)/1=(y-2)/2=(z-3)/3, which one of the following is...
Text Solution
|
Find the value of m for which thestraight line 3x-2y+z+3=0=4x=3y+4z+1 ...
Text Solution
|
The intercept made by the plane vec rdot vec n=q on the x-axis is ...
Text Solution
|
Equation of a line in the plane pi-=2x-y+z-4=0 which is perpendicul...
Text Solution
|
If the foot of the perpendicular from the origin to plane is P(a ,b...
Text Solution
|
The equation of the plane which passes through the point of interse...
Text Solution
|
Let A( vec a)a n dB( vec b) be points on two skew lines vec r= vec a+...
Text Solution
|
Let A(1,1,1),B(23,5)a n dC(-1,0,2) be three points, then equation of a...
Text Solution
|
The point on the line (x-2)/1=(y+3)/(-2)=(z+5)/(-2) at a distance of 6...
Text Solution
|
The coordinates o the foot of the perpendicular drawn from the orig...
Text Solution
|
about to only mathematics
Text Solution
|
The length of projection of the line segment joining the points (1,...
Text Solution
|
The number of planes that are equidistant from four non-coplanar po...
Text Solution
|
In a three-dimensional coordinate system, P ,Q ,a n dR are images o...
Text Solution
|
A plane passing through (1,1,1) cuts positive direction of coordinates...
Text Solution
|
If lines x=y=za n dx=y/2=z/3 and third line passing through (1,1,1) fo...
Text Solution
|
Find the point of intersection of line passing through (0,0,1) and t...
Text Solution
|
Shortest distance between the lines (x-1)/1=(y-1)/1=(z-1)/1a n d(x-...
Text Solution
|
Distance of point P(vecP) from the plane vecr.vecn=0 is
Text Solution
|