Two vectors and lie in the –plane

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

Problem

Two vectors

\mathbf{P}

and

\mathbf{Q}

lie in the

xy

–plane. Their magnitudes are

P

and

Q

and they make angles

\alpha

and

\beta

respectively with the

x

–axis. (i) Explain, without performing any numerical calculation, how each vector can be expressed in rectangular component form. (ii) If the rectangular components of

\mathbf{P}

and

\mathbf{Q}

are denoted by

(P_x, P_y)

and

(Q_x, Q_y)

respectively, write the expressions for the rectangular components of the resultant vector

\mathbf{R}=\mathbf{P}+\mathbf{Q}

and justify each term in your expressions. (iii) Using only geometrical reasoning, show why the magnitude and direction of

\mathbf{R}

obtained from the component method must agree with the result given by the triangle law of vector addition.

Related theory

Vectors
Vector Operations
Vector Algebra
Components of a vector

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