Magnitude and direction of a vector. Applications
Knowing the magnitude of a vector tells you how much; knowing its direction tells you which line it moves along. By combining both ideas you can solve very different problems: from the distance between two points to whether two forces pull along the same line.
Magnitude of a vector and distance between points
Calculate the magnitude of the vector $\vec{v} = (3, -4)$.
Calculate the magnitude of the vector $\vec{v} = (3, -4)$.
Find the exact distance between the points $A(-2, 5)$ and $B(4, -3)$.
Find the exact distance between the points $A(-2, 5)$ and $B(4, -3)$.
Unit vector
Obtain a unit vector that has the same direction and sense as the vector $\vec{w} = (-5, 12)$.
Obtain a unit vector that has the same direction and sense as the vector $\vec{w} = (-5, 12)$.
Vectors with the same direction: finding a vector given its magnitude
A drone travels in a straight line according to the vector $\vec{d} = (k, 6)$. If the total distance travelled is $10$ metres, calculate the possible values of the…
A drone travels in a straight line according to the vector $\vec{d} = (k, 6)$. If the total distance travelled is $10$ metres, calculate the possible values of the parameter $k$.
Find the coordinates of a vector $\vec{v}$ knowing that its magnitude is $5\sqrt{2}$ and that it has the same direction and sense as the vector $\vec{u} = (-1, 1)$.
Find the coordinates of a vector $\vec{v}$ knowing that its magnitude is $5\sqrt{2}$ and that it has the same direction and sense as the vector $\vec{u} = (-1, 1)$.
Resultant of several vectors
Two coplanar forces represented by the vectors $\vec{F}1 = (30, -40)$ N and $\vec{F}2 = (-15, 20)$ N act on a body. Calculate the magnitude of the resultant force…
Two coplanar forces represented by the vectors $\vec{F}_1 = (30, -40)$ N and $\vec{F}_2 = (-15, 20)$ N act on a body. Calculate the magnitude of the resultant force $\vec{R} = \vec{F}_1 + \vec{F}_2$ and determine a unit vector in the direction of this resultant.
Three coplanar forces maintain an object in static equilibrium at the origin of coordinates (that is, the resultant force is the zero vector). The components of two of…
Three coplanar forces maintain an object in static equilibrium at the origin of coordinates (that is, the resultant force is the zero vector). The components of two of them are known: $\vec{F}_1 = (40, 30)$ N and $\vec{F}_2 = (-20, 50)$ N. Calculate the components of the third force $\vec{F}_3$ and its exact magnitude.