What is the projection of <6,−4,8> onto <−1,3,−7>?

1 Answer
Narad T.
Jul 21, 2017

The vector projection is =−7459<−1,3,−7>
The scalar projection is =−61√59

Explanation:

Let →b=<6,−4,8> and →a=<−1,3,−7>

The vector projection of →b over →a is

=→a.→b∣∣∣∣→a∣∣∣∣2⋅→a

The dot product is

→a.→b=<6,−4,8>.<−1,3,−7>=(6⋅−1)+(−4⋅3)+(8⋅−7)

=−6−12−56=−74

The modulus of →a is

||<−1,3,−7>||=√1+9+49=√59

Therefore,

The vector projection is

=−7459<−1,3,−7>

The scalar projection is

=→a.→b∣∣∣∣→a∣∣∣∣=−61√59

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