Three vectors →a, →b, and →c each have a magnitude of 50 m and lie in an xy plane. their directions relative to the positive direction of the x axis are 30°, 195°, and 315°, respectively. what are (a) the magnitude and (b) the angle of the vector →a+→b+→c and (c) the magnitude and (d) the angle of →a−→b+→c? what are the (e) magnitude and (f) angle of a fourth vector →d such that (→a+→b)−(→c+→d)=0 ?

(a): 37.94 m.

(b):

(c): 126.957 m.

(d):

(e): 49.92 m.

(f):

Explanation:

Given:

Any vector , making an angle with respect to the positive x-axis, can be written in terms of its x and y components as follows:

where, are the unit vectors along the x and y axes respectively.

Therefore, the given vectors can be written as

(a):

(b):

Direction can be found as follows:

The negative sign indicates that the sum of the vectors is below the positive x axis.

Therefore, direction of this vector sum counterclockwise with respect to positive x-axis =

(c):

(d):

Direction can be found as follows:

(e):

(f):

Direction can be found as follows:

The x component of this vector is negative and y component is positive therefore the vector lie in second quadrant, which means, the direction of this vector, counterclockwise with respect to positive x axis =