Vector ( P =a

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

Problem

Vector

\mathbf{P}=a\,\mathbf{\hat{i}}+b\,\mathbf{\hat{j}}

is added to vector

\mathbf{Q}=Q\bigl(\cos\alpha\,\mathbf{\hat{i}}+\sin\alpha\,\mathbf{\hat{j}}\bigr)

. Their resultant

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

has magnitude

R

and is directed at

45^{\circ}

above the positive

x

-axis. Attempt the following parts in order. (i) Express the

x

- and

y

-components of

\mathbf{R}

in terms of the unknowns

a

and

b

as well as the known quantities

Q,\alpha

and

R

. (ii) Hence derive general expressions for

a

and

b

in terms of

Q,\alpha,R

. (iii) If

Q=6\,\text{N}

\alpha = 120^{\circ}

and

R=8\,\text{N}

, calculate the numerical values of

a

and

b