# Worksheet: Geometric and Physical Applications of Vectors

Q1:

Given that and , find .

• A
• B
• C
• D

Q2:

The forces , , and are acting on a particle, where and are two perpendicular unit vectors. Determine the magnitude the forcesβ resultant, , and its direction to the nearest minute.

• A ,
• B ,
• C ,
• D ,

Q3:

Rectangle has vertices , , , and . Use vectors to determine its area.

Q4:

If and , find .

• A
• B
• C
• D

Q5:

A book moves on a horizontal plane after being pushed by a force of 12 N parallel to the plane. The friction force between the book and the plane is 5 N. Find the resultant of these forces, and express it in terms of , the unit vector in the direction of the bookβs motion.

• A N
• B N
• C N
• D N

Q6:

The forces , , and act on a particle, where and are two perpendicular unit vectors. Given that the forcesβ resultant , determine the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q7:

The resultant of forces , , and , makes an angle with the positive -axis. Determine , the magnitude of the resultant, and the value of .

• A ,
• B ,
• C ,
• D ,
• E ,

Q8:

Given that , , and their resultant , determine the values of and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q9:

All the sides of rhombus are of length 5. Suppose that and that . Use vector multiplication to find the lengths of the two diagonals.

• A ,
• B ,
• C ,
• D ,

Q10:

is a square, in which the coordinates of the points , , and are , , and . Use vectors to determine the coordinates of the point and the area of the square.

• A , area
• B , area
• C , area
• D , area

Q11:

Given that and , determine the area of the parallelogram whose adjacent sides are represented by and .

Q12:

Trapezium has vertices , , , and . Given that and , find the area of that trapezium.

Q13:

Given a trapezium , in which and , find the value of such that .

• A
• B8
• C
• D

Q14:

is a rectangle, in which the coordinates of the points , , and are , , and , respectively. Use vectors to find the value of and the coordinates of point .

• A ,
• B ,
• C ,
• D ,
• E ,

Q15:

Given the information in the diagram below, find the value of such that .

• A
• B
• C
• D

Q16:

Given a triangle , in which , , and , use vectors to determine the length of .

• A cm
• B cm
• C cm
• D cm

Q17:

In the given figure, and are parallel lines; however, is NOT parallel to either or . Given that , , and , determine whether and are in the same, opposite, or different directions.