Home
Class 12
MATHS
Find the equation of a line : passing th...

Find the equation of a line : passing through the point `vec c` , parallel to the plane `vec r *vec n = p` and intersecting the line `vec r =vec a + t vec b`.

Text Solution

Verified by Experts

The correct Answer is:
`vecr =vecc + k [ vecc-veca) xx vecc - veca) xx vecb )]`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the equation of a line: passing through the point vec c ,parallel to the plane vec r*vec n=p and intersecting the line vec r=vec a+tvec b

The equation of a line passing through the point vec a parallel to the plane vec r*vec n=q and perpendicular to the line vec r=vec b+tvec c is a.vec r=vec a+lambda(vec n xxvec c) b.(vec r-vec a)xx(vec n xxvec c) c.vec r=vec b+lambda(vec n xxvec c) d.none of these

Find the vector and cartesian equation of the line passing through the point P (1,2,3) and parallel to the planes : vec(r).(hati - hatj + 2 hatk) = 5. vec(r).(3hati + hatj + hatk) = 6.

The vector equation of the plane passing through the origin and the line of intersection of the planes vec rdot vec a=lambdaa n d vec rdot vec b=mu is a. vec rdot(lambda vec a-mu vec b)=0 b. vec rdot(lambda vec b-mu vec a)=0 c. vec rdot(lambda vec a+mu vec b)=0 d. vec rdot(lambda vec b+mu vec a)=0

Find the equation of a plane passing through the line of intersection of the planes vec r*(2i-j+k)=5 and vec r*(3i+j-k)=6 and parallel to x axis.

Show that equation of the plane passing through a point having position vector vec(a) and parallel to vec(b) and vec(c) is vec(r) = vec(a) + lambda vec(b) + mu vec(c) .

A line l is passing through the point vec b and is parallel to vector vec c Determine the distance of point A(vec a) from the line l in the form vec b-vec a+((vec a-vec b)vec c)/(|vec a|^(2))vec c or (|(vec b-vec a)xxvec c|)/(|vec c|)

The length of the perpendicular form the origin to the plane passing through the point a and containing the line vec r= vec b+lambda vec c is a. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c+ vec cxx vec a|) b. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c|) c. ([ vec a vec b vec c])/(| vec bxx vec c+ vec cxx vec a|) d. ([ vec a vec b vec c])/(| vec cxx vec a+ vec axx vec b|)

Find the equation of a straight line in the plane vec r* vec n=d which is parallel to vec r= vec a+lambda vec b and passes through the foot of the perpendicular drawn from point P( vec a)to vec rdot vec n=d(w h e r e vec ndot vec b=0)dot a. vec r= vec a+((d- vec a*vec n)/(n^2))n+lambda vec b b. vec r= vec a+((d- vec a* vec n)/n)n+lambda vec b c. vec r= vec a+(( vec a* vec n-d)/(n^2))n+lambda vec b d. vec r= vec a+(( vec a* vec n-d)/n)n+lambda vec b

The length of the perpendicular from the origin to the plane passing through the points vec a and containing the line vec r=vec b+lambdavec c is