Question

Two vectors in space are equal only if they have equal component in

• A. A given direction
• B. Two given directions
• C. Three given directions
• D. In any arbitrary direction

Answer 1

Answer: (C)

Three given directions

Let $\overline{a}$ and $\overline{b}$ be two vectors.
Hence
$\overline{a}=a_{x}i+a_{y}j+a_{z}k$

Similarly
$\overline{b}=b_{x}i+b_{y}j+b_{z}k$

Where $i,j,k$ are unit vectors along $x,y$ and $z$ axes.

For the vectors $\overline{a}$ and $\overline{b}$ to be equal, ie
$\overline{a}=\overline{b}$
$a_x=b_x$
$a_y=b_y$
$a_z=b_z$
Hence answer is option $C$.