### Video Transcript

Find the direction cosines of the
vector 𝐀 with components five, two, and eight.

We recall that if vector 𝐯 has
components 𝐯 sub 𝑥, 𝐯 sub 𝑦, and 𝐯 sub 𝑧 and direction angles 𝛼, 𝛽, and 𝛾,
then the direction cosines cos of 𝛼, cos of 𝛽, and cos of 𝛾 are equal to 𝐯 sub
𝑥 over the magnitude of 𝐯, 𝐯 sub 𝑦 over the magnitude of 𝐯, and 𝐯 sub 𝑧 over
the magnitude of 𝐯, respectively, where the magnitude of vector 𝐯 is equal to the
square root of 𝐯 sub 𝑥 squared plus 𝐯 sub 𝑦 squared plus 𝐯 sub 𝑧 squared.

In this question, we are told that
vector 𝐀 has components five, two, and eight. The magnitude of vector 𝐀 is
therefore equal to the square roots of five squared plus two squared plus eight
squared. Five squared is equal to 25, two
squared is equal to four, and eight squared is equal to 64. Summing these three values gives us
an answer of 93. Therefore, the magnitude of vector
𝐀 is the square root of 93. This means that the cos of angle 𝛼
is equal to five over the square root of 93, the cos of angle 𝛽 is equal to two
over the square root of 93, and, finally, the cos of angle 𝛾 is equal to eight over
the square root of 93. The direction cosines of vector 𝐀
are five over the square root of 93, two over the square root of 93, and eight over
the square root of 93.