Show that the points A,B,C with position vectors `(3hat(i)- 2 hat(j)+ 4hat(k)),(hat(i) + hat(j) +hat(k))` and `(-hat(i)+ 4 hat(j)- 2 hat(k))` respectively 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 points, A, B and C having position vectors (2hat(i)-hat(j)+hat(k)), (hat(i)-3hat(j)-5hat(k)) and (3hat(i)-4hat(j)-4hat(k)) respectively are the vertices of a rightangled triangle. Also, find the remaining angles of the triangle.

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 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(i)+9hat(j)+4hat(k) and 4(-hat(i)+hat(j)+hat(k)) respectively are coplanar.

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 vectors -hat(i) + hat(j) - hat(k), hat(i) + hat(j) + hat(k) and hat(i) + hat(k) are coplanar.

The position vectors of A, B, C are 2hat(i)+hat(j)-hat(k), 3hat(i)-2hat(j)+hat(k) and hat(i)+4hat(j)-3hat(k) respectively. Show that A, B and C 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.