Question

Let A and B be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angles 30° and 60° respectively, find the resultant.

Answer 1

magnitude of vector A = magnitude of vector B = 10 unit.

vector A inclined to the x - axis at angle 30° and vector B inclined to the x -axis at angle 60°.

so, angle between vector A and vector B = (60° - 30°) = 30°

now, |A + B| = $\sqrt{A^2+B^2+2ABcos\theta}$

where $\theta$ indicates angle between vector A and vector B.

so, resultant of A and B = √{10² + 10² + 2 × 10 × 10cos30°}

= √{100 + 100 + 200 × √3/2}

= √{200 + 100√3}

= 10√{2 + √3} units

hence, resultant = 10√(2 + √3) units.

Answer 2

Resultant of vector A and vector B is 10√(2+√3).

Explanation is given in the picture