Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
In this lesson, we will learn how to use vectors and operations on them to solve problems.
Q1:
Given that β π£ = 1 7 β π π΄ and β π£ = 8 β π π΅ , find β π£ π΅ π΄ .
Q2:
The forces β πΉ = οΊ β 4 β π + 6 β π ο 1 N , β πΉ = οΊ β 9 β π + 4 β π ο 2 N , and β πΉ = οΊ β 4 β π β 3 β π ο 3 N are acting on a particle, where β π and β π are two perpendicular unit vectors. Determine the magnitude the forcesβ resultant, π , and its direction π to the nearest minute.
Q3:
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 β π , the unit vector in the direction of the bookβs motion.
Q4:
All the sides of rhombus π π΅ πΆ π΄ are of length 5. Suppose that s i n β π΄ π π΅ = 3 4 and that π΄ π΅ > π πΆ . Use vector multiplication to find the lengths of the two diagonals.
Q5:
Given that , , , and are four collinear points, where , determine the value of which satisfies .
Q6:
π΄ π΅ πΆ π· is a square, in which the coordinates of the points π΄ , π΅ , and πΆ are ( 1 , β 8 ) , ( 3 , β 1 0 ) , and ( 5 , β 8 ) . Use vectors to determine the coordinates of the point π· and the area of the square.
Q7:
The forces β πΉ = β 1 0 β π β 7 β π 1 , β πΉ = π β π β β π 2 , and β πΉ = 5 β π + ( π β 1 0 ) β π 3 act on a particle, where β π and β π are two perpendicular unit vectors. Given that the forcesβ resultant β π = β 1 3 β π β 3 β π , determine the values of π and π .
Q8:
Given the information in the diagram below, find the value of π such that ο π΄ π· + ο π· πΈ = π ο π΄ πΆ .
Q9:
The resultant of forces β πΉ = οΊ β 4 β π + 2 β π ο 1 N , β πΉ = οΊ 5 β π β 7 β π ο 2 N , and β πΉ = οΊ 2 β π + 9 β π ο 3 N , makes an angle π with the positive π₯ -axis. Determine π , the magnitude of the resultant, and the value of t a n π .
Q10:
Given a trapezium π΄ π΅ πΆ π· , in which π΄ π· β₯ π΅ πΆ and π΄ π· π΅ πΆ = 7 , find the value of π such that ο π΄ πΆ + ο π΅ π· = π ο π΄ π· .
Q11:
In the given figure, β ο© ο© ο© ο© β π΄ π΅ and β ο© ο© ο© ο© β πΆ π· are parallel lines; however, β ο© ο© ο© ο© ο© β π π is NOT parallel to either β ο© ο© ο© ο© β π΄ π΅ or β ο© ο© ο© ο© β πΆ π· . Given that πΈ β π΄ π΅ , πΉ β πΆ π· , and π β π π , determine whether ο« π π and ο« π π are in the same, opposite, or different directions.
Q12:
Given that β πΉ = 8 β π β 5 β π 1 , β πΉ = β 1 5 β π β 5 β π 2 , and their resultant β π = β π β π β π β π , determine the values of π and π .
Q13:
Given that β π΄ = ( β 2 , 7 ) and β π΅ = ( 3 , β 8 ) , determine the area of the parallelogram whose adjacent sides are represented by β π΄ and β π΅ .
Q14:
If β π£ = β 7 6 β π π΄ π΅ and β π£ = β 5 β π π΄ , find β π£ π΅ .
Q15:
π΄ π΅ πΆ π· is a rectangle, in which the coordinates of the points π΄ , π΅ , and πΆ are ( β 1 8 , β 2 ) , ( β 1 8 , β 3 ) , and ( β 8 , π ) , respectively. Use vectors to find the value of π and the coordinates of point π· .
Q16:
Given a triangle π΄ π΅ πΆ , in which π΄ π΅ = 7 c m , π΅ πΆ = 5 6 c m , and π β π΄ π΅ πΆ = 1 2 0 β , use vectors to determine the length of π΄ πΆ .
Q17:
Trapezium π΄ π΅ πΆ π· has vertices π΄ ( 4 , 1 4 ) , π΅ ( 4 , β 4 ) , πΆ ( β 1 2 , β 4 ) , and π· ( β 1 2 , 9 ) . Given that ο π΄ π΅ β«½ ο π· πΆ and ο π΄ π΅ β ο πΆ π΅ , find the area of that trapezium.
Donβt have an account? Sign Up
