For the vector Squareroot 22 1 find the magnitude and direc

For the vector (-Squareroot 22. - 1), find the magnitude and direction angle (to the nearest tenth) Give measure of the direction angle as an angle in (0, 360 degree).

Solution

  You are given x and y end points of a vector starting at (0, 0).

|v| = (x² + y²) = ( (22)² + (-1)² ) = 23 ====> 4.7958 Ans. Magnitude

= arctan (y / x) = arctan (-1 / 23) = -12.03°

x and -y, so angle is in quadrant IIi, so we must subtract 180° to get true . because in qudarant - 180 or 270 -
= --12.03° - 180° = -192.03° or 270° -( -12.03°) ==> 270° +12.03° ===> 282.03° Ans. direction

|v| = 4.7958 -192.03° or 4.7958 282.03°