Given that and , find .
The forces , , and are acting on a particle, where and are two perpendicular unit vectors. Determine the magnitude the forces’ resultant, , and its direction to the nearest minute.
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 book’s motion.
All the sides of rhombus are of length 5. Suppose that and that . Use vector multiplication to find the lengths of the two diagonals.
Given that , , , and are four collinear points, where , determine the value of which satisfies .
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.
The forces , , and act on a particle, where and are two perpendicular unit vectors. Given that the forces’ resultant , determine the values of and .
Given the information in the diagram below, find the value of such that .
The resultant of forces , , and , makes an angle with the positive -axis. Determine , the magnitude of the resultant, and the value of .
Given a trapezium , in which and , find the value of such that .
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.
Given that , , and their resultant , determine the values of and .
Given that and , determine the area of the parallelogram whose adjacent sides are represented by and .
If and , find .
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 .
Given a triangle , in which , , and , use vectors to determine the length of .
Trapezium has vertices , , , and . Given that and , find the area of that trapezium.