# Two vectors with magnitudes of 4 meters and 3 meters cannot have a resultant of?

0

(a) 3 meters

(b) 4 meters

(c) 7 meters

(d) 8 meters

Thanks i hate vectors.

• The maximum value shows when the vectors act in the SAME direction.

———————–>4m

————–>3m

So the resultant = 4 + 3 = 7m

(If you go 4m forward and another 3m forward, you will be 7m away from your starting point.)

The minimum value shows up when the vectors act in OPPOSITE directions.

———————–>4m

3m<———–

Resultant = 4 – 3 = 1m

(or 3 – 4 = -1m if you like)

(If you go 4m forward and 3m reverse, you will be 1m ahead.

If you go 3m forward and 4m reverse, you will be 1m behind.)

So any value out of the range of 1m to 7m is wrong. So 8m is the answer.

• for two vectors a and b having an angle x in between the value of resultant is the square root of a^2+b^2+2ab cosx

so for vectors 4 and 3 any value between 1(for x=0) and 7(for x=180)

can be obtained.so the value not possible is 8

ans…….d

• For any two vectors A and B with |A| >= |B|, the following is true:

|A| – |B| =< |A+B| =< |A| + |B|

Here, |A| = 4m and |B| = 3m. Thus:

(4m) – (3m) =< |A+B| =< (4m) + (3m)

1m =< |A+B| =< 7m

So, any value between 1m and 7m inclusive can be obtained. Since 8m is outside that range, the two vectors can not have a sum of 8m (D).

• any value at or between 1m and 7m is in play.

1m is when the vectors are antiparallel, and 7m is when the vectors are parallel. any other value in between can be obtained depending on the value of the angle between the two vectors

so that answer is (d).

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