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In this lesson, we will learn how to express a vector in component form given its initial and terminal points.

Q1:

Find the components of the vector 𝐴 𝐵 , where 𝐴 = ( − 4 . 5 , 1 . 2 ) and 𝐵 = ( − 4 . 5 , 5 . 7 ) .

Q2:

Find the coordinates of the terminal point of the vector in the given diagram.

Q3:

Find the coordinates of the initial point of the vector in the given diagram.

Q4:

Find the components of the vector 𝐴 𝐵 , where 𝐴 = ( 1 . 5 , − 0 . 3 ) and 𝐵 = ( − 1 , 5 ) .

Q5:

A vector has components and a terminal point . What is its initial point?

Q6:

Find the components of the vector .

Q7:

The initial point of the vector shown in the diagram is the origin, .

What are the coordinates of its terminal point?

What are the components of the vector?

Q8:

Q9:

Q10:

Consider the vector in the given diagram.

What are the coordinates of its initial point?

Q11:

Q12:

Q13:

Q14:

Q15:

Suppose the coordinates of points and are and respectively. Find the components of the vector in terms of , , , and .

Q16:

A vector has components and an initial point . What is its terminal point?

Q17:

Find the components of the vector , where and .

Q18:

Q19:

Given that the coordinates of 𝐴 and 𝐵 are ( − 1 2 , − 2 4 ) and ( − 3 , 1 6 ) respectively, find ‖ ‖ 𝐴 𝐵 ‖ ‖ .

Q20:

Q21:

What is the magnitude of the vector 𝐴 𝐵 , where 𝐴 = ( 9 . 1 , − 2 . 3 ) and 𝐵 = ( 7 . 7 , 2 . 5 ) ?

Q22:

Using the shown graph, determine the position vector of point 𝐶 relative to the origin point 𝑂 , denoted by 𝑂 𝐶 , and find its norm, denoted by ‖ ‖ 𝑂 𝐶 ‖ ‖ .