15.If the vectors `vec(a)=2hat(i)-hat(j)+hat(k),vec(b)=hat(i)+2hat(j)-3hat(k)` and `vec(c)=3hat(i)+phat(j)+5hat(k)` are coplanar,then find `P`

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

Three vectors vec(A) = 2hat(i) - hat(j) + hat(k), vec(B) = hat(i) - 3hat(j) - 5hat(k) , and vec(C ) = 3hat(i) - 4hat(j) - 4hat(k) are sides of an :

a. Prove that the vector vec(A)=3hat(i)-2hat(j)+hat(k) , vec(B)=hat(i)-3hat(j)+5hat(k), and vec(C )=2hat(i)+hat(j)-4hat(k) from a right -angled triangle. b. Determine the unit vector parallel to the cross product of vector vec(A)=3hat(i)-5hat(j)+10hat(k) & =vec(B)=6hat(i)+5hat(j)+2hat(k).

If the vectors vec (a) = 2 hat (i) - hat (j) + hat (k) , vec ( b) = hat (i) + 2 hat (j) - 3 hat (k) and vec(c ) = 3 hat (i) + lambda hat (j) + 5 hat (k) are coplanar , find the value of lambda

Consider three vectors vec(A)=2 hat(i)+3 hat(j)-2 hat(k)" " vec(B)=5hat(i)+nhat(j)+hat(k)" " vec(C)=-hat(i)+2hat(j)+3 hat(k) If these three vectors are coplanar, then value of n will be

Find lambda so that the vectors vec a=2 hat i- hat j+ hat k ,\ vec b= hat i+2 hat j-3 hat k\ a n d\ vec c=3 hat i+lambda hat j+5 hat k are coplanar.

If vectors vec a= hat i+2 hat j- hat k , vec b=2 hat i- hat j+ hat k and vec c=lambda hat i+ hat j+2 hat k are coplanar, then find the value of (lambda-4) .

Determine lambda such that a vector vec(r) is at right angles to each of the vectors vec(a) = lambda hat(i) + hat(j) + 3hat(k), vec(b) = 2hat(i) + hat(j) - lambda hat(k), vec(c) = -2hat(i) + lambda hat(j) + 3hat(k) .

If vec(A)=2hat(i)+hat(j)+hat(k) and vec(B)=hat(i)+hat(j)+hat(k) are two vectors, then the unit vector is

Find the projection of vec(b)+ vec(c ) on vec(a) where vec(a)= 2 hat(i) -2hat(j) + hat(k), vec(b)= hat(i) + 2hat(j)- 2hat(k), vec(c ) = 2hat(i) - hat(j) + 4hat(k)