For example, you and a friend might both be pulling on strings attached to a single block of wood.
Find the magnitude and direction of the resultant force in the following circumstances.a) The first force has a magnitude of 10 N and acts east.
Remember, $\mathbf.\mathbf=|a|^2$, and if two vectors are perpendicular, their scalar product is $0$.
Magnitude and direction Some vector problems involve a vector function which tells you how an object's position changes in time, for example.
In simple terms, lines are represented using vectors by specifying a point on the line with a position vector, and then using a direction vector to specify the direction of the line.
In the same way that $y=mx c$ specifies a line that passes through $(0,c)$ and has gradient $m$, the vector equation $\mathbf=\mathbf \lambda\mathbf$ specifies a line that passes through the point with position vector $\mathbf$ in the direction of $\mathbf$.(moderate) Two displacements with magnitudes of 10 m and 12 m can be combined to form resultant vectors with many different magnitudes.Which of the following magnitudes can result from these two displacments? For the possible resultants, what angle exists between the original displacements? (moderate) A bicycle tire (Radius = R = 0.4 m) rolls along the ground (with no slipping) through three-quarters of a revolution.We are very used to expressing lines using cartesian geometry in the form $y=mx c$ and other variants.The vector equation of a line is no more complicated really, it's just a case of getting used to it.This short article aims to highlight some of the powerful techniques that can be used to solve problems involving vectors, and to encourage you to have a go at such problems to become more familiar with vector properties and applications. When we first meet them, it's often in the context of transformations - a translation can be expressed as a vector telling us how far something is translated to the right (or left) and up (or down).Confusion can strike when we come across vectors being used to indicate absolute position relative to an origin as well as showing a direction.It stays at rest for a while then moves 300 m at 34° "south of west" (this means 214° from the x-axis.) Find the total displacement of the car.4.(easy) Two forces are being exerted on an object, but in different directions.For me, diagrams make it much easier to make sense of what is going on - I can represent a position vector as a point on the diagram with a line segment coming from the origin.Direction vectors just become line segments joined onto other vectors, with a helpful arrow to remind me that $\mathbf$ and $\mathbf$ are in opposite directions!