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.`

Statement 1: Line (x-1)/1=(y-0)/2=(z+2)/(-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

If vec axx vec b= vec bxx vec c!=0,\ then show that vec a+ vec c=m vec b ,\ w h e r e\ m is any scalar.

Let vec r be a unit vector satisfying vec rxx vec a= vec b ,w h e r e| vec a|=sqrt3a n d| vec b|=sqrt2. Then

Statement 1: In "Delta"A B C , vec A B+ vec A B+ vec C A=0 Statement 2: If vec O A= vec a , vec O B= vec b ,t h e n vec A B= vec a+ vec b

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

Write the condition for the lines vec r= vec a_1+lambda vec b_1 a n d\ vec r= vec a_2+mu vec b_2dot\ to be intersecting.

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