Show that the points whose position vectors are `(5hat(i) + 6 hat(j) + 7 hat(k)), ( 7 hat(i) - 8hat(j) + 9 hat(k)) and (3 hat(i) + 20 hat(j) + 5 hat(k))` are collinear.

Show that the points whose position vectors are 2hat(i) + 3hat(j) - 5hat(k), 3hat(i) + hat(j) - 2hat(k) and 6hat(i) - 5hat(j) + 7hat(k) are collinear.

Show that the points whose position vectors are 5hat(i) + 5 hat(k), 2 hat(i) + hat(j) + 3 hat(k) and -4 hat(i) + 3 hat(j) - hat(k) are collinear.

show that the points whose position vectors are (-2hat(i) +3hat(j) +5hat(k)) (hat(i)+2hat(j)+3hat(k)) " and " (7hat(i) -hat(k)) are collinear.

Show that the points whose position vectors are -2hat(i)+3hat(j)+5hat(k),hat(i)+2hat(j)+3hat(k) and 7hat(i)-hat(k) are collinear.

If three points A, B and C with position vectors hat(i) + x hat(j) +3 hat(k) , 3 hat(i) + 4 hat(j) + 7hat( k) and y hat(i) - 2 hat(j) - 5 hat(k) respectively are collinear, then (x,y) =

Show that the following points whose position vectors are given are collinear : (i) 5 hat(i) + 5 hat(k), 2 hat(i) + hat(j) + 3 hat(k) and - 4 hat(i) + 3 hat(j) - hat(k) (ii) - 2 hat(i) + 3 hat(j) + 5 hat(k), hat(i) + 2 hat(j) + 3 hat(k) and 7 hat(i) - hat(k) .

Find the value of lambda , if the point with position vectors 3hat(i) - 2hat(j) - hat(k), 2hat(i) + 3hat(j) - 4hat(k), -hat(i) + hat(j) + 2hat(k) and 4hat(i) + 5hat(j) + lambda hat(k) are coplanar.

Show that the poins whose position vectors are 4hat(i)+5hat(k),hat(i)+hat(j)+3hat(k)" and "-5hat(i)+3hat(j)-hat(k) are collinear.

If A,B,C and D are points whose position vectors are hat(i) + hat(j) + hat(k), 4hat(i) - hat(j) + 2hat(k), 5hat(i) + hat(j) , 7 hat(i) + 2hat(j) + 3hat(k) respectively, then the projection of AB on CD is

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.