Test: Resolution of Vectors - ACT MCQ

A vector can be resolved in number of components. But, the number of components has to be equal to the number of independent directions available. It can only be resolved into independent directions no matter how many they are.

The vertical component of any vector with magnitude a is a sin θ. Here θ = 60. sin θ = ½. Hence the answer is 50/2 = 25 N.

 The standard for is a(cos θ î + sin θ ĵ). Here, a = 5, and θ = 45 degrees. When we substitute this in the equation, we get, the resolved vector as 

The splitting of a vector into two component vectors is called vector resolution. The vector can be resolved into as many components as there are independent directions.

The magnitude of any vector can be found by taking the square root of sum of the squares of its two components. Hence, the sum of the squares of components is equal to 4² + 3² = 25. Square root of 25 = 5. Hence, the answer is 5.

The horizontal component of any vector with magnitude a is a cos θ. Here θ = 60. cos θ = ½. Hence the answer is 5/2 = 2.5 m/s.

The correct answer is a(cos θ î + sin θ ĵ). This is obtained by constructing a right-angled triangle with the distance of the point from the origin with either of the axes and then finding out the corresponding values for X and Y components.

Concept:

Resolution of vectors into components: We have a vector (F) where the magnitude of the vector is F and the angle with horizontal is θ.

The vector has two components: 1. Vertical component and 2. Horizontal component

Vertical component (F_y) = F Sinθ

Horizontal component (F_x) = F Cosθ 
Calculation:
The horizontal component is responsible to move the stone along the ground.

F_x = 60cos60°  = 30 N

Hence, the effective value of the pull tending to move the stone on the ground is 30 N.

Concept:

Resolution of vectors into components: We have a vector (F) where the magnitude of the vector is F and the angle with horizontal is θ.

The vector has two components: 1. Vertical component and 2. Horizontal component

Vertical component (F_y) = F Sinθ

Horizontal component (F_x) = F Cosθ 
Calculation:
Given that:

Fx = 50N , θ = 60°

F_x = Fcosθ

Fy = Fsinθ

Concept:

• Resolution of vectors is the process of splitting a vector into two or more vectors in such a way that their combined effect is the same as that of the given vectors.
  • The vectors into which the given vector is split are called Components of vectors.

Explanation:​

• Resolution of vectors into components: We have a vector (F) where the magnitude of the vector is F and the angle with horizontal is θ.

The vector has two components: 1. Vertical component and 2. Horizontal component

Vertical component (F_y) = F Sinθ

Horizontal component (F_x) = F Cosθ