Let the forces be F1 and F2 at an angle A and their resultant be F. According to question,

| F1 | = | F2 | = | F |

We know,

F^2 = F1^2 + F2^2 + 2 F1 F2 cos A

or, F^2 = F^2 + F^2 + 2 F F cos A

or, F^2 - 2F^2 = 2 F^2 cos A

or, - F^2 = 2 F^2 cos A

or, -1 = 2 cos A

or, cos A = -1/2

or, cos A = cos 120

So, A = 120 degrees.

Hence, when two forces of equal magnitude act at an angle of 120 degrees, the resultant is equal to one of the forces.

No, it is not necessary that a physical quantity that has magnitude and direction be a vector quantity.But yes a vector quantity should have magnitude and direction and apart from that, it should also follow vector laws of addition. One eg. for a quantity that has magnitude and direction but does not follow vector laws of addition is electric current.

Yes, a physical quantity can have magnitude and direction but still be a scalar if it doesn't obey the vector addition. An example is Electric Current which has magnitude and a fixed direction, but it does not follow vector laws of addition.

Any vector directed in two dimensions can be thought of as havingtwo different components. The component of a single vector describes the influence of that vector in a given direction.

Yes, if the angle between the two vectors is more than 90^obut less than 270⁰. (cosΘ is negative)

If a vector A is multiplied by a real number (say n), the vector of same nature is obtained but its magnitude is n times that of A.

The two vectors (say A and B) of different magnitudes cannot be combined togive zero resultant since minimum value of combination isІA-BІ which is not zero if AB.

The three vectors A, B and Cof different magnitudes can be zero such that they form a closed triangle, then,

A+B+C=0

or, C=-(A+B)

Hence, the sum of three vectors may be zero if vector sum of any two vectors is equal and opposite to the third vector.

Note: The vectors can give this result only if they lie in the same plane. If three...

Yes, a vector which has zero magnitude is also a vector in case of two vectors travelling in opposite directions with equal magnitudes. At this case, the resultant vector has zero magnitude but it is still a vector. We call it a null vector.

No, if three vectors do not lie in a plane, they cannot give zero resultant.

Explanation:

Let A, B and Cbe three vectors. If they give zero resultant, then

A+B+C=0

or, A= -(B+C)

Hence, they will produce zero resultant, if Ais equal to negative of vector (B+C). The vector (B+C) lies in the plane of B and C.Hence, Awill be equal to negative of (B+C) if A,B and C all lie in a plane.

A negative of a vector represents the direction opposite to the reference direction. It means that the magnitude of two vectors are same but they are opposite in direction.

For example, if A and B are two vectors that have equal magnitude but opposite in direction, then vector A is negative of vector B.

Torque has the dimension of force times distance, symbolically T²L²M. Although those fundamental dimensions are the same as that for energy or work, official SI literature suggests using the unit newton metre (Nm) and never the joule.

The y component is a number such that

20^2 + y^2

= 20^2 or y^2

= 400 - 144

= 256

= 16^2 so the y component is 16 m/s and the angle is acos(12/20) = acos(3/5)

= acos(0.6) = approx 53.1 degrees.

Numerical Physics

Parallelogram Law of Vector Addition Formula

Consider two vectors P and Q with an angle θ between them. The sum of vectors P and Q is given by the vector R, the resultant sum vector using the parallelogram law of vector addition. If the resultant vector R makes an angleϕwith the vector P, then the formulas for its magnitude and direction are:

• |R| = (P²+ Q²+ 2PQ cos θ)
• β = tan^-1[(Q sin θ)/(P + Q cos θ)]

Parallelogram Law of Vector Addition Proof

Let us first see the statement of the...

If vectors are arranged as trigonal planar and have equal magnitude, it is an ideal case of zero resultant.