Express `2overset^^i-overset^^j+3overset^^k` as the sum of a vector parallel and a vector perpendicular to `2overset^^i+4overset^^j -2 overset^^k`

Find a unit vector along the vector oversetrarrb =3 overset^^i -overset^^j + overset^^k

The scalar product of the vector overset^^i+overset^^j+overset^^k with a unit vector along the sum of the vectors 2overset^^i+4overset^^j-5overset^^k"and" lambdaoverset^^i+2overset^^j+3overset^^k is equal to I.Find the value of lambda .

Find the projection of the vector oversetrarra =2overset^^i+overset^^j -3 overset^^k on the vector. oversetrarrb =-overset^^i+3overset^^j-overset^^k

Find the unit vector in the direction of the vector oversetrarra=overset^^i+overset^^j+2overset^^k .

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

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 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 .

Compute the magnitude of oversetrarrb=2overset^^i-7overset^^j-3overset^^k ,vector

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 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