Question

Find the scalar and vector projections of b onto a. a = −2, 3, 6 , b = 4, −1, 6

Answer 1

|a|=42+72+(−4)2−−−−−−−−−−−−−√

=16+49+16−−−−−−−−−−√

=81−−√

=9

Explanation:

Find the dot product

a⋅b=(4,7,−4)⋅(3,−1,1)

=4⋅3+7⋅(−1)+(−4)⋅1

=12−7−4

=1

Find the magnitude of a

|a|=42+72+(−4)2−−−−−−−−−−−−−√

=16+49+16−−−−−−−−−−√

=81−−√

=9

Scalar projection of b on to a is given by

compab=a⋅b|a|

Substitute the values of the a⋅b and |a|, to get

compab=19

Vector projection of b onto a is given by

projab=[compab]a|a|

Substitute the values of the compab and |a|, to get

projab=[19](4,7,−4)9=(481,781,−481)

Result: compab=19projab=(481,781,−481)