Question

4)If two vectors are given as A= -11i+2j (m) and B= 3i+3j (m), determine the resultant vector R=3A-B/2, and also find its magnitude R and direction?

Answer 1

Answer on Question #58828 – Math – Analytic Geometry

Question

4) If two vectors are given as $A = -11i + 2j$ (m) and $B = 3i + 3j$ (m), determine the resultant vector $R = 3A - B/2$, and also find its magnitude $R$ and direction?

Solution

The resultant vector is

$$R = 3A - B/2 = 3(-11i + 2j) - 1/2 \cdot (3i + 3j) = -33i + 6j - 1.5i - 1.5j = -34.5i + 3.5j$$

Its magnitude: $|R| = \sqrt{(-34.5)^2 + (3.5)^2} = \sqrt{1202.5} \approx 34.68$

Direction cosines of vector R are the cosines of the angles between the vector R and the two coordinate axes:

$$\cos(\alpha) = \frac{-34.5}{\sqrt{(-34.5)^2 + (3.5)^2}} \approx -0.995;$$ $$\alpha \approx 174.2{}^\circ;$$ $$\cos(\beta) = \frac{3.5}{\sqrt{(-34.5)^2 + (3.5)^2}} \approx 0.101;$$ $$\beta \approx 84.21{}^\circ.$$

Direction: NW

Answer: $-34.5i + 3.5j$; 34.68; NW.

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