Statement 1: Line `(x-1)/1=(y-0)/2=(z2)/(-1)` lies in the plane `2x-3y-4z-10=0.` Statement 2: if line ` vec r= vec a+lambda vec b` lies in the plane ` vec rdot vec c=n(w h e r en` is scalar`),t h e n vec bdot vec c=0.`

Write the position vector of the point where the line vec r= vec a+lambda vec b meets the plane vec r dot (vec n)=0.

Write the equation of the plane containing the lines vec r= vec a+lambda vec b\ a n d\ vec r= vec a+mu vec c

Write the equation of the plane vec r= vec a+lambda vec b+mu vec c\ in scalar product form.

veca , vec b , vec c are non-coplanar vectors and x vec a + y vec b + z vec c = vec 0 then

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

prove that | vec axx vec b|=( vec adot vec b)t a ntheta, w h e r e theta is the angle between vec a a n d vec bdot

The equation of the plane containing the parallel lines vec r=vec a+tvec c and vec r=vec b+phivec c is

If | vec axx vec b|=4,\ | vec adot vec b|=2,\ t h e n\ | vec a|^2| vec b|^2= 6 b. 2 c. 20 d. 8

Solve the simultaneous vector equation of vec x and vec y, vec x + vec c xxvec y = vec a, vec y + vec c xxvec x = vec b where vec c! = 0

The line of intersection of the planes vec r*(3vec i-vec j+vec k)=1 and vec r*(vec i+4vec j-2vec k)=2, is