Question

(a) What is the sum of the following four vectors in unit-vector notation? For that sum, what are (b) the magnitude, (c) the angle in degrees, and (d) the angle in radians? Positive angles are counterclockwise from the positive direction of the x axis; negative angles are clockwise.
: 6.00 m at + 0.900 rad
: 5.00 m at - 75.0°
: 4.00 m at + 1.20 rad
: 6.00 m at - 210°

Answer 1

6m at 0.9 radian means 6m at $51.57^0$

Since positive angles are counter clockwise

6m at $51.57^0$ can be written as 6*cos$51.57^0$i+6*sin$51.57^0$j = 3.73i+4.70j

5m at $-75^0$ can be written as 5*cos$(-75)^0$i+5*sin$(-75)^0$j = 1.294i-4.83j

4m at 1.2 radian means 4m at $68.75^0$

4m at $68.75^0$ can be written as 4*cos$68.75^0$i+4*sin$68.75^0$j = 1.45i+3.73j

6m at $-210^0$ can be written as 6*cos$(-210)^0$i+6*sin$(-210)^0$j = -5.20i-3j

a) So sum of the vector = 1.274i+0.6j

b) Magnitude = $\sqrt{1.274^2+0.6^2} = 1.98 m$

c) Angle,  $tan\theta = \frac{0.6}{1.274} \\ \\ \theta = 25.22^0$