Video Transcript
The vector 𝐯 is shown on the grid
of units squares below. Find the value of the magnitude of
𝐯.
We know that the magnitude of any
vector is its length. By creating a right triangle on the
grid, we can see that the vector has moved four units to the right and three units
up. The magnitude of vector 𝐯 can
therefore be found using Pythagoras’s theorem. This states that the length of the
hypotenuse is equal to the sum of the squares of the two shorter sides. The magnitude of 𝐯 is therefore
equal to the square root of 𝑎 squared plus 𝑏 squared.
Whilst it doesn’t matter which
order we substitute the four and the three, we usually do the horizontal component
first. Four squared is equal to 16, and
three squared is equal to nine. The magnitude of vector 𝐯 is equal
to the square root of 25. As 25 is a square number, we can
calculate this. The square root of 25 is equal to
positive or negative five. As we’re dealing with a length, our
answer must be positive. Therefore, the magnitude of vector
𝐯 on the grid is five.
