The projections of the vector A on the coordinate axes Ax = -4, Y = 4, Az = 2 are given

The projections of the vector A on the coordinate axes Ax = -4, Y = 4, Az = 2 are given. Find the length and direction cosines of the vector A.

The projections of the vector on the coordinate axes are the coordinates of this vector, then its module will be equal to:

| A | = √ (-4) ^ 2 + 4 ^ 2 + 2 ^ 2) = √ (16 + 16 + 4) = 6.

The cosines of the tilt angles are:

with axis oX cos (a) = -4 / 6 = -2/3;

with axis oY cos (b) = 4/6 = 2/3;

with oZ axis cos (c) = 2/6 = 1/3.