Question

Given that vector c=a-b , vector c has a magnitude of 10 units and direction 270, vector a has a magnitude of 2 units and direction 150.
A) write the vector c in terms of unit vectors i,j,k.
B) write the vector a in terms of unit vectors i,j,k.
C) write the vector b in terms of unit vectors i,j,k.
D) find the magnitude and direction of the vector b.

Answer 1

Question #74302, Physics / Other

Given that vector $c = a - b$, vector $c$ has a magnitude of 10 units and direction 270, vector $a$ has a magnitude of 2 units and direction 150.

A) write the vector $c$ in terms of unit vectors $i,j,k$.

B) write the vector $a$ in terms of unit vectors $i,j,k$.

C) write the vector $b$ in terms of unit vectors $i,j,k$.

D) find the magnitude and direction of the vector $b$.

Solution

A) Vector components are determined as follows.

$$\begin{array}{l} c_x = 10 \times \cos 270{}^\circ = 0 \\ c_y = 10 \times \sin 270{}^\circ = -10 \\ c = -10j \\ \end{array}$$

B) $a_x = 2 \times \cos 150{}^\circ = -1.73$

$$\begin{array}{l} a_y = 2 \times \sin 150{}^\circ = 1 \\ a = -1.73i + j \\ \end{array}$$

C) $b = a - c = -1.73i + j - (-10j) = -1.73i + 11j$

D) Vector magnitude is calculated as follows.

$$\begin{array}{l} \text{magnitude} = \sqrt{\left(-1.73\right)^2 + 11^2} = 11.14 \\ \text{direction} = \cos^{-1}\left(\frac{-1.73}{11.14}\right) = 98.93{}^\circ \\ \end{array}$$

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