00:01
The magnitude of a vector is given to be 12 .0 units and its direction is given by 30 degrees counterclockwise with respect to the positive x -axis.
00:23
And the magnitude of b is given to be 15 .0 units and its direction is given to be 15 .0 units and its direction is given by 45 degrees counterclockwise with respect to the positive x axis and the magnitude of vector c is given to be 17 .0 units and its direction is given to be 30 degrees clockwise with respect to the negative y axis these three vectors can be drawn in the xy plot as the resultant r vector is given by the sum of the vectors a, b and c.
01:20
And here the x component of the resultant can be written as a cos 30 degrees plus b cause 45 degrees minus c sine 30 degrees.
01:40
Substituting for a, b and c we get 12 .0 multiplied by cost 30 degrees plus 15 .0 multiplied by cost 45 degrees minus 17 .0 multiplied by sine 30 degrees.
02:03
On calculating, we get 12 .4989 units.
02:13
Similarly, the x, sorry, the y component of the resultant can be written as a sign 30 degrees plus b sign 45 degrees minus c cost 30 degrees.
02:34
Now substituting for a, b and c we get 12 .0 multiplied by sine 30 degrees plus 15 .0.
02:45
Multiplied by sine 45 degrees minus 17 .0 multiplied by cost 30 degrees now on calculating we get 1 .841 units now the magnitude of the result can be written as square of sorry square root of the sum of the square of each common now substituting for rx in ry we get 12 .4989 the whole square plus 1 .881 the whole square...