Answer:
|a|=42+72+(−4)2−−−−−−−−−−−−−√
=16+49+16−−−−−−−−−−√
=81−−√
=9
Step-by-step 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)
