Addition Of A System Coplanar Forces - Free MCQ Practice Test with solutions,

A scalar is any positive or negative physical quantity that can be completely specified by its magnitude. Examples of scalar quantities include length, mass, time, etc.

For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents their magnitude and direction of the line of action respectively. The head/tip of the arrow indicates the sense of direction of the vector.

If a vector is multiplied by a scalar then its magnitude is increased by amount of that scalar’s magnitude. When multiplied by a negative scalar it going to change the directional sense of the vector.

All the vectors quantities obey parallelogram law of addition. Two vectors A and B (can be called as component vectors) are added to form a resultant vector. R = A+B.

The component along x-axis is the cosine component of the vector. And the y-axis component of the vector is sine component, if the angle is being made with the x-axis. And 180- α for some of the trigonometric function may change their sign.

tan θ = P/B
         = x component / y component 

The sine and the cosine components of the given vectors considering the angle B as the only angle of consideration comes 1.5m and 2.59m.

After getting the cosine components of the given vectors we obtain the total length of the x-axis components to be 3cos60 + 2cos30 = 3.23.

Yes, the magnitude of the resultant of the two vectors always depends on the angle between them. It might be greater or smaller than one of the vector’s length. For perfectly saying, it does depends upon the angle between them.

The vectors are mutually perpendicular, this means that the angle between the forces is 90 degree. Thus the resultant will form at 45 degrees to any of the vector.

 If one is heading towards positive X-axis and the other is in the other direction opposite to the first one, with both having the same length and having an angle between them being obtuse, means that the direction is to be in the direction of either 1st quadrant or in the 4th quadrant.

As it is a force vector, it means it is going to have a direction and a magnitude. The magnitude is not the square root of R, R is just the magnitude of the vector given.

As one can imagine three vectors coming out of a single point and are having a 120 degree angle with their adjacent ones, the resultant would be zero.

The vector is made by joining the final and the starting point. If we consider any arbitrary point then the length would be calculated w.r.t the starting point, which might give different magnitude but same direction.