Find the equation of a line through a po...

Find the equation of a line through a point C of position vector `vec c=3veci+2vecj` and perpendicular to the vector `vecb=veci-vecj` in the xy-plane.

Text Solution

Verified by Experts

The correct Answer is:

`vecr=(3+m)hati+(2+m)hatj`, where m is a scalar

Topper's Solved these Questions

UNITS AND DIMENSION
NN GHOSH|Exercise EXERCISE|26 Videos
VELOCITY OF SOUND
NN GHOSH|Exercise EXERCISE|26 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the plane through the point 2veci+3vecj-veck and perpendicular to the vector 3veci-4vecj+7veck .

Find the equation of a line which passes through a given point of position vector vec c and is parallel to a given vector vecb .

Find the equation of the plane through the 2veci+3vecj-veck and perpendicular to the vector 3veci+2vecj-2vecj . Determine the perpendicular distance of this plane from the origin.

Find the equation of the plane through the point 2veci-vecj+veck and perpendiulr to the vector 4veci+2vecj-3veck . Determine the perpendicular distance of this plane from the origin.

Find the vector equation of a line passing through the point with position vector (2 hati - 3 hatj - 5 hatk) and perpendicular to the plane vec(r). (6 hati - 3 hatj - 5 hatk) + 2 = 0. Also find the point of intersection of this line and the plane.

Find the equation of a plane passing throug the piont A(3,-2,1) and perpendicular to the vector 4veci+7vecj-4veck . If PM be perpendicular from the point P(1,2,-1) to this plane find its length.

A non zero vector veca is parallel to the line of intersection of the plane determined by the vectors veci,veci+vecj and the plane determined by the vectors veci-vecj, veci+veck find the angle between veca and the vector veci-2vecj+2veck .

Find the direction cosines and unit vector along the vector vecr=2veci+vecj+3veck .

Find the vector equation of the through the points 2veci+vecj-3veck and parallel to vector veci+2vecj+veck

NN GHOSH-VECTOR AND SCALARS-All Questions

Prove that for a vector veca defined by veca=axveci+ayvecj+azveck, the...
Text Solution
|
If vecb and vec c be the intersecting face-diagonals of a cube of edge...
Text Solution
|
Show that the position vector of a place on the surface of the earth w...
Text Solution
|
A man rows a boat with a speed 10 m/s along N-E direction. The shore l...
Text Solution
|
A force vecF=5veci+2vecj+veck displaces a body from a point with coord...
Text Solution
|
If the sum and difference of two vectors are at right angles, show tha...
Text Solution
|
Prove that (vecaxxvecb)^2=veca^2b^2-(veca.vecb)^2.
Text Solution
|
Show that if two vectors are equal in magnitude, their vector sum and ...
Text Solution
|
Find the area of the parallelogram whose sides are represented by 2h...
Text Solution
|
Show that (veca+vecb)xx(veca-vecb)=-2(vecaxxvecb) and use this result ...
Text Solution
|
Find the equation of a line through a point C of position vector vec c...
Text Solution
|
Find the moment of a force , vecF=3veci+2vecj acting at point vecr=vec...
Text Solution
|
If vecP+vecQ=vecR and vecP-vecQ=vecS, prove that vecR^2+vecS^2=2(vecP^...
Text Solution
|
Show that a vector remains invariant (unchanged ) under rotation of co...
Text Solution
|
Find the components of a vector vecA=2hati+3hatj along the directions ...
Text Solution
|
The force on a positively charged particle is given by vecF=qvecE+qvec...
Text Solution
|
A point P lies on a vector veca.the position vector of the point is ve...
Text Solution
|
Show that if vecu.(dvecu)/(dt)=0 the vector vecu is of constant magnit...
Text Solution
|
If veca=m vecb+vec c, find the scalar m.
Text Solution
|
Using vector method prove that in any triangle ABC a^2=b^2+c^2-2bc cos...
Text Solution
|