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 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.

Find the value of 'x' such that four points with position vectors : A(3hat(i)-2hat(j)+hat(k)), B(4hat(i)+x hat(j)+5hat(k)), C(4hat(i)+2hat(j)-2hat(k)) and D(6hat(i)+5hat(j)-hat(k)) are coplanar.

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.

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.

The position vectors of the point A, B , C and D are 3hat(i)-2hat(j)-hat(k), 2hat(i)+3hat(j)-4hat(k), -hat(i)+hat(j)+2hat(k) and 4hat(i)+5hat(j)+lambdahat(k) respectively. If A, B, C, D are coplanar, then lambda=

Show that the vectors hat(i)-3hat(j)+4hat(k),2hat(i)-hat(j)+2hat(k)and 4hat(i)-7hat(j)+10hat(k) are coplanar.

Show that the vectors hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2hat(i)-5hat(j)+3hat(k) are coplanar.

Find the value of lambda for which the four points with position vectors (-hat(j)+hat(k)), (2hat(i)-hat(j)-hat(k)), (hat(i)+lambda hat(j)+hat(k))and (3hat(j)+3hat(k)) are coplanar.