Question

Find the projection of the vector a on the vector b if:

(a) a =2i + 3j - 7k and b= 4i - 2j + 3k

Answer 1

The projection is,

`proj_(b) a = (-76/29)i+(38/29)j-(57/29)k`

Explanation:

We find the magnitude of a and b,

`|a| = √(2^2+3^2+7^2)\\ |a| = √(4+9+49) \\|a| = √(62 )`

And,

`|b| = √(4^2+2^2+3^2)\\ |b| = √(16+4+9)\\ |b| = √(29)`

Now, finding the scalar product between a and b,

`a.b = (2)(4)+(3)(-2)+(-7)(3)\\a.b = -19\\`

Now, the projection formula is,

`proj_(b) a = ((a.b)/(|a|^2))(a)\\so,\\proj_(b) a = (-19)/(√(29)^2 )(4i-2j+3k)\\proj_(b) a = -19/29(4i-2j+3k)\\proj_(b) a = -76/29i+38/29j-57/29k`

Hence we have the answer