Find aunit vector along the sum of the vectors `oversetrarra = overset^^i-3overset^^k "and"oversetrarrb =2overset^^i+5overset^^j-3overset^^k?`

Are the vectors oversetrarra =2 overset^^i -overset^^j "and"oversetrarrb =overset^^i+2overset^^j equal?

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

Find the angle between the vectors " " oversetrarra=overset^^i+overset^^j-overset^^k " and "oversetrarrb=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 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

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

Consider the vectors oversetrarra=2overset^^i+3overset^^j+overset^^k " and " oversetrarrb=3overset^^i +2 overset^^j -3overset^^k find oversetrarra.oversetrarrb

Consider the vectors oversetrarra=2overset^^i+3overset^^j+moverset^^k " and " oversetrarrb=3overset^^i +2 overset^^j -3overset^^k Find the value of m for which oversetrarra "and"oversetrarrb are perpendicular. In such a case verify that (oversetrarra+oversetrarrb)^2=|oversetrarra""^2|+|oversetrarrb""^2|

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.