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Ques: Which of the following is the vertical component of the vector v with direction angle 405° and the magnitude
Components Of A Vector
Definition Of Components Of A Vector
Any two-dimensional vector can be said to have an influence in two different directions. Thus we can say it has two parts. Each of these two parts-one horizontal, and the other, vertical-is known as component.
More About Components of a Vector
The horizontal and vertical components of a vector v are given as |v| cos θ and |v| sin θ respectively, where θ is the angle made by v with positive x-axis in the clockwise direction.
Video Examples: Components of Vectors
Example of Components of a Vector
Solved Example onComponents of a Vector
Ques: Which of the following is the vertical component of the vector v with direction angle 405° and the magnitude
?
Choices:
A. 4
B.
C. 8
D.
Correct Answer: A
Solution:
Step 1: The vertical component of v whose direction angle is θ = |v| sin θ
Step 2: = sin 405° [Substitute |v| = , θ = 405°.]
Step 3: = × () = 4.