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

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

Find lambda if the vectors overset^^i-overset^^j+overset^^k,3overset^^i+overset^^j+2overset^^k " and " overset^^i+lambdaoverset^^j-3overset^^k are coplanar.

Area of a rectangle having vertices A,B,C and D with position vectors -overset^^i+1/2overset^^j+4overset^^k,overset^^i+1/2overset^^j+4overset^^k,overset^^i-1/2overset^^j+4overset^^k"and"-overset^^i-1/2overset^^j+4overset^^k respectively is : a) 1/2 b)1 c)2 d)4

Show that the vectors veca=overset^^i-2overset^^j+3overset^^k,vecb=-2overset^^i+3overset^^j-4overset^^k and vecc=overset^i-3overset^j+5overset^^k are coplanar.

Show that the points A,B and C with position vectors oversetrarra =3overset^^i-4overset^^j-4overset^^k," " oversetrarrb= 2overset^^i-overset^^j+overset^^k " and " oversetrarrc=overset^^i-3overset^^j-5overset^^k respectively form the vertices of a right angled triangle.

Show that the vectors 2overset^^i-3overset^^j+4overset^^k"and " -4overset^^i+6overset^^j-8overset^^k are collinear.

Consider the points A,B,C,D with position vectors overset^^i+2overset^^j+8overset^^k,3overset^^j+4overset^^k,overset^^i+overset^^j+3overset^^k and 2overset^^i+7overset^^k respectively. Prove that ABCD is parallelogram

Show that the points A(-2overset^^i+3overset^^j +5overset^^k),B(overset^^i+2overset^^j+3overset^^k)"and"C(7overset^^i- overset^^k) are collinear.

Consider the points A,B,C,D with position vectors overset^^i+2overset^^j+8overset^^k, 3overset^^j+4overset^^k,overset^^i+overset^^j+3overset^^k and 2overset^^i+7overset^^k respectively. Find the position vector of the mid point of AC

Consider the points A,B,C,D with position vectors overset^^i+2overset^^j+8overset^^k,3overset^^j+4overset^^k,overset^^i+overset^^j+3overset^^k and 2overset^^i+7overset^^k respectively. Find the position vector of the mid point of BD