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 =

answer: the direction of the wind is expressed as the direction from which the wind is blowing. for example, easterly winds blow from east to west, while westerly winds blow from west to east.

explanation: