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)]

Let us first see the statement of the...

pressure is a scalar quantity,not a vector quantity. It has a magnitude but no direction associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular to the surface.

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.

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.

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.

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.

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...

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.

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

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.