Help your students prepare for their Maths GCSE with this free column vectors worksheet of 20+ questions and answers
Column vectors describe a movement. The top number of a column vector is the x component – it tells us where to move in the x direction (right and left). The bottom number is the y component – it tells us where to move in the y direction (up and down). For example, the column vector of 3 on top of negative 4 in large round brackets describes a movement of 3 in the positive x direction (right) and 4 in the negative y direction (down).
A column vector can be multiplied by a scalar. When multiplying a vector by a scalar, we multiply both components of the vector by the scalar. Two vectors are parallel if one is a scalar multiple of the other. Multiplying a vector by -1 would give a vector of the same length but in the opposite direction.
We can perform vector addition and subtraction with column vectors. To do this, we add or subtract the x components of each vector and then add or subtract the y components.
The magnitude of a vector is its length. The magnitude of a column vector can be found using Pythagoras’ Theorem. By drawing lines representing the x component and y component of the vector, we can construct a right angle triangle. The magnitude is the length of the hypotenuse of the triangle formed.
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