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`

Find veca.(vecbxxvecc) ,if veca=2overset^^i+overset^^j+3overset^^k.vecb=-overset^^i+2overset^^j+overset^^k and vecc=3overset^^i+overset^^j+2overset^^k .

Find the volume of the following parallelo-piped whose the coterminal edges are: veca=overset^^i-2overset^^j+3overset^^k,vecb=2overset^^i+overset^^j+overset^^k"and" vecc=2overset^^i+overset^^j-overset^^k

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.

Find the volume of a parallelepiped with coterminal edges represented by vectors veca=2overset^^i+3overset^^j+4overset^^k, vecb=3overset^^i-overset^^j+2overset^^k "and" vecc=overset^^i+2overset^^j-overset^^k .

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.

Find the sum of the vectors oversetrarra =overset^^i-2overset^^j+overset^^k,oversetrarrb=-2overset^^i+4overset^^j+5overset^^k " and " oversetrarrc=overset^^i-6overset^^j-7overset^^k

Let " "veca=overset^^i+4overset^^j+2overset^^k, vecb=3overset^^i-2overset^^j+7overset^^k"and" vecc=2overset^^i-overset^^j+4overset^^k. Find a vector vecd perpendicular to both veca"and"vecb"and"vecc.vecd=15 .

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.

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

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