Vectors and (magnitude

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Vectors

\mathbf{A}=7\,\hat i-4\,\hat j

and

\mathbf{B}

(magnitude

10\,\text{N}

, directed

30^{\circ}

below the positive

x

-axis) are given. A third vector

\mathbf{C}

satisfies

2\mathbf{A}+\mathbf{B}+\mathbf{C}=\mathbf{0}

. Calculate the magnitude and direction of

\mathbf{C}

(direction to be given as the angle made with the positive

x

-axis, measured anticlockwise). (a)

24\,\text{N}

120^{\circ}

(b)

26\,\text{N}

330^{\circ}

(c)

26\,\text{N}

150^{\circ}

(d)

18\,\text{N}

150^{\circ}