Let two non-zero vectors and act consecutively in the same plane.

MATHEMATICS · Multi-part · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Let two non-zero vectors

\mathbf{a}

and

\mathbf{b}

act consecutively in the same plane. (i) State the triangle law of vector addition. (ii) Using position vectors, explain logically why

\mathbf{a}+\mathbf{b}=\mathbf{b}+\mathbf{a}

for any two vectors in the plane. (iii) In a triangle

ABC

, suppose

\overrightarrow{AB}=\mathbf{a}

and

\overrightarrow{BC}=\mathbf{b}

. Express the vector

\overrightarrow{AC}

in terms of

\mathbf{a}

and

\mathbf{b}

, and verify that the statement obtained is consistent with the triangle law mentioned in part (i).