Show that the four points A, B, C and D with position vectors`4 hat i+5\ hat j+ hat k ,-(\ hat j+ hat k),3 hat j+9\ hat j+4 hat k\ a n d\ 4( hat i+ hat j+ hat k)`, respectively are coplanar.

Show that the points A, B,C and D with positions vectors 4 hat i +5 hat j + hat k, -( hat j + hat k), 3 hat i + 9 hat j + 4 hat k and -4 hat i + 4 hat j + 4 hat k respectively are coplanar.

Show that the four points A, B, C and D with position vectors 4hat(i) + 5hat(j) + hat(k) - hat(j) - hat(k), 3hat(i) + 9hat(j) + 4hat(k) and 4(-hat(i) + hat(j) + hat(k)) respectively are coplanar.

Show that the four points A,B,C and D with position vectors 4hat i+5hat j+hat k,-(hat j+hat k),3hat j+9hat j+4hat k and 4(-hat i+hat j+hat k) respectively are coplanar.

Show that the four points with position vectors 4 hat i+8 hat j+12 hat k ,\ 2 hat i+4\ hat j+6 hat k ,3 hat i+5\ hat j+4 hat k\ a n d\ 5 hat i+8\ hat j+5 hat k are coplanar.

Show that the four points A, B, C and D with position vectors 4hat(i)+5hat(j)+hat(k), -(hat(j)+hat(k)),3hat(i)+9hat(j)+4hat(k) and 4(-hat(i)+hat(j)+hat(k)) respectively are coplanar.

Prove that the four points 4 hat i +5 hat j +hat k, -(hat j+hat k) ,3 hat i+ 9 hat j +4hat k and 4(-hat i+hat j + hat k) are coplanar.

Consider the 4 points A, B, C and D with position vectors 4 hat i + 8 hat j + 12 hat k, 2 hat i + 4 hat j + 6 hat k , 3 hat i + 5 hat j + 4 hat k and 5 hat i + 8 hat j ++ 5 hat k . (i) Find vec(AB), vec(AC), vec (AD) (ii) Show that the 4 points are coplanar.

Show that the point A , B and C with position vectors vec a =3 hat i - 4 hat j -4 hat k vec b = 2 hat i j + hat k and vec c = hat i - 3 hat j - 5 hat k , respectively form the vertices of a right angled triangle.

Show that the four points with position vectors 4hati+8 hat j +12hat k, 2 hat i+4hat j +6hat k, 3 hat i +5hat j +4hatk and 5hat i+8hat j+5hatk are coplanar.