If a is perpendicular to b and p is non-zero scalar such that `pr+(r*b)a=c`, then r satisfy

If vec a is perpendicular to vec b and vec r is non-zero vector such that p vec r+( vec rdot vec a) vec b= vec c , then vec r= vec c/p-(( vec adot vec c) vec b)/(p^2) (b) vec a/p-(( vec cdot vec b) vec a)/(p^2) vec a/p-(( vec adot vec b) vec c)/(p^2) (d) vec c/(p^2)-(( vec adot vec c) vec b)/p

Given that veca is a perpendicular to vecb and p is a non zero scalar, solve for barr when p vecr+(vecr.vecb)veca=vecc .

Let a, b and c be non-zero vectors and |a|=1 and r is a non-zero vector such that r times a=b and r*a=1 , then

If c is a given non-zero scalar, and vec A and vec(B) are given non-zero vector such that vec A_|_ vecB , then find vector vec X which satisfies the equation vec Adot vec X =c and vec Axx vec X= vec Bdot

If vec a and vec b are two given vectors and k is any scalar, then find the vector vec r satisfying vec rxx vec a+k vec r= vec b .

If a,b and c are three non-zero vectors such that no two of these are collinear. If the vector a+2b is collinear with c and b+3c is collinear with a( lamda being some non-zero scalar), then a+2b+6c is equal to

If vec b is not perpendicular to vec c , then find the vector vec r satisfying the equyation vec rxx vec b= vec axx vec b and vec r. vec c=0.

If c is a given non - zero scalar, and vecA and vecB are given non- zero , vectors such that vecA bot vecB . Then find vector, vecX which satisfies the equations vecA.vecX =c and vecA xx vecX =vecB .

If a,b,c be non-zero vectors such that a is perpendicular to b and c and |a|=1,|b|=2,|c|=1,b*c=1 and there is a non-zero vector d coplanar with a+b and 2b-c and d*a=1 , then minimum value of |d| is

In Figure, each of P A ,\ Q B ,\ R C and S D is perpendicular to l . If A B=6c m , B C=9c m , C D=12 c m and P S=36 c m , then determine P Q ,\ Q R and R S .