Find the value of x for which `x(overset^^i+overset^^j+overset^^k)` is a unit vector.

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 values of x,y and z so that oversetrarra =x overset^^I +y overset^^j +z overset^^k "and" oversetrarrb =overset^^I - 2 overset^^j +3 overset^^k are equal?

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

Compute the magnitude of oversetrarra =overset^^i+overset^^j+overset^^k ,vector

Find the values of x and y so that the vectors 2overset^^i+3overset^^j "and" xoverset^^i+yoverset^^j are equal.

Find a vector of magnitude 5 units and parallel to the resultant of the vectors veca=2overset^^i+3overset^^j-overset^^k "and "vecb=overset^^i-2overset^^j+overset^^k .

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

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

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|