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

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

1 Answer

3 votes

Answer:

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

User MarmiK
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