Question

find a vector whose magnitude is 4 which makes angles pie / 4 with x-axis pie/ 3 with y axis and then obtuse angle with Z axis​

Answer 1

Let the vector be "s". Then it's components are sx, sy and sz.

It is given that |s| = 4.

We know that sx = s cos π/4

= 4/√2

= 2√2

in the same way sy= s cos π/3

= s × 1/2

= 4/2 = 2

now |s|square = (sx)square + (sy)square + (sz)square

(4) square = (2√2) square + (2)square + (sz)square

16 = 8 + 4 + (sz)square

(sz)square = 16-12

= 4

sz = 2

Hence the vector is 2√2 ¡ + 2j + 2k.

Hope it helps.