Find the angle between the two planes whose vector equations are `vec r.(9vec i+ 6vecj -2veck)=11` and `vec r.(6vec i- 2vecj +3veck)=13`

Find the angle between the planes whose vector equations are vec r.(2 hat i+2 hat j-3 hat k)=5 and vec r.(3 hat i-3 hat j+5 hat k)=3 .

Find the cosine of the angle between the planes vecr.(2veci-3vecj-6veck)=7 and vecr.(6veci+2vecj-9veck)=5

Find the angle between two vectors vec a and vec b , if | vec a xx vec b|= vec a . vec b .

Find the angle between two vectors vec a\ a n d\ vec b , if | vec axx vec b|= vec adot vec bdot

If a vector vecr of magnitude 3sqrt6 is directed along the bisector of the angle between the vectors veca =7veci-4vecj -4veck and vecb = -2veci- vecj+ 2veck , then vecr is equal to

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

Find the value of the constant lamda so that vectors veca=vec(2i)-vecj+veck, vecb=veci+vec(2j)-vec(3j), and vecc=vec(3i)+vec(lamdaj)+vec(5k) are coplanar.

Find the angle between two vectors vec a and vec b with magnitudes sqrt(3) and 2 respectively having vec a. vec b=sqrt(6)

If the two adjacent sides of two rectangles are represented by vectors vec p=5 vec a-3 vec b ; vec q=- vec a-2 vec b \ and \ vec r=-4 vec a- vec b ; vec s=- vec a+ vec b , respectively, then the angel between the vector vec x=1/3( vec p+ vec r+ vec s) \ and \ vec y=1/5( vec r+ vec s) is a. -cos^(-1)((19)/(5sqrt(43))) b. cos^(-1)((19)/(5sqrt(43))) c. pi-cos^(-1)((19)/(5sqrt(43))) d. cannot be evaluate

Find the angle between the vectors vec a\ a n d\ vec b where: vec a= hat i+2 hat j- hat k ,\ vec b= hat i- hat j+ hat k