Video: Finding the Norm of Vectors

If 𝐀 = (βˆ’2, 1, 0) and 𝐁 = (2, 0, 4), determine |𝐀| + |𝐁|.

02:25

Video Transcript

If vector 𝐀 is equal to negative two, one, zero and vector 𝐁 is equal to two, zero, four, determine the magnitude of vector 𝐀 plus the magnitude of vector 𝐁.

Let’s firstly consider the general vector 𝑃 with coordinates π‘₯, 𝑦, and 𝑧. The magnitude or modulus of this vector is equal to the square root of π‘₯ squared plus 𝑦 squared plus 𝑧 squared. In this question, vector 𝐀 is equal to negative two, one, zero. This means that the magnitude of vector 𝐀 is equal to the square root of negative two squared plus one squared plus zero squared. Negative two squared is equal to four. One squared is equal to one. And zero squared is equal to zero. Four plus one plus zero is equal to five. Therefore, the magnitude of vector 𝐀 is equal to root five.

Vector 𝐁 has coordinates two, zero, four. This means that the magnitude of vector 𝐁 is equal to the square root of two squared plus zero squared plus four squared. Two squared is equal to four. And four squared is equal to 16. Therefore, the magnitude of vector 𝐁 is the square root of 20. This is equal to two root five. This is because the square root of 20 is equal to the square root of four multiplied by the square root of five. The square root of four is equal to two. Therefore, the square root of 20 equals two multiplied by the square root of five.

We were asked to calculate the magnitude of vector 𝐀 plus the magnitude of vector 𝐁. This is equal to root five plus two root five. As root five is the same as one root five, our final answer is three root five. If 𝐀 equals negative two, one, zero and 𝐁 equals two, zero, four, then the magnitude of 𝐀 plus the magnitude of 𝐁 is equal to three root five.

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