Show that the vectors `2overset^^i-overset^^j+overset^^k, overset^^i-3overset^^j-5overset^^k and 3overset^^i-4overset^^j-4overset^^k` form the vertices of a right angled trainagle.

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

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.

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.

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.

Find the angle between the vectors overset^^i-2overset^^j+3overset^^k"and"3overset^^i-2overset^^j+overset^^k.

The position vectors of the points A,B,C are given to be 2overset^^i+overset^^j-overset^^k,overset^^3i-overset^^2j+overset^^k"and" 1overset^^i+4overset^^j-3overset^^k respectively.Prove that A,B,C are collinear

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.

Find [veca" " vecb" " vecc] "if "veca=overset^^i-2overset^^j+overset^^k, vecb=2overset^^i-3overset^^j+overset^^k" and "vecc =3overset^^i+overset^^j-2overset^^k

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.