Which vector has the greatest magnitude?
We begin by recalling that the magnitude of a vector is its length. In this question, we’re given five vectors 𝐚 to 𝐞 and need to determine which has the greatest magnitude, in other words, which vector has the longest length.
By inspection, we can see that this is vector 𝐜, as we move two units vertically downwards and five units horizontally to the left. The vector which has the greatest magnitude is vector 𝐜. And we can denote this vector with a half arrow as shown.
Whilst it is not required in this question, we could calculate the magnitude of this vector using our knowledge of the Pythagorean theorem. As we have a right triangle, the magnitude or length of vector 𝐜 is equal to the square root of two squared plus five squared. This is equal to the square root of four plus 25, which is the square root of 29. The magnitude of vector 𝐜 is root 29.