Question

Write the projections of vector r = 3i - 4j + 12 k on the coordinate axes.

Answer 1

x - axis = \(\hat i\)

y - axis = \(\hat j\)

z - axis = \(\hat k\)

Proj \(\vec b\)^{\(\vec a\)} =  \(\cfrac{\vec a.\vec b}{|\vec b|^2}\vec b\)

Projection along x - axis = \(\cfrac31\hat i\)

= 3 \(\hat i\)

Projection along y - axis = \(\cfrac{-4}1\hat j\)

= -4 \(\hat j\)

Projection along z - axis  = \(\cfrac{12}1\hat k\)

 = 12 \(\hat k\)