If X be a vector 3 X represents  3 added to X  3 times of X  the ratio of X and 3  None

The correct option is;

3 times of X

Explanation:

The algebraic properties of a vector are;

Multiplicative identity for real numbers 1

1P = P for each P

Scalar associative property = r(sP) = (rs)P

Scalar distributive property (r + s)P = rP + sP

Vector distributive property r(P + Q) = rP + rQ

Additive inverse of a vector such that a vector P has an inverse -P such that we have;

P + (-P) = 0

Vector associative property (P + Q) + R = P + (Q + R)

Vector commutative property P + Q = Q + P.

measuring things 1 litre of water

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.