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Sagot :
Its Scalar projection [tex]\sqrt{2}[/tex] and Vector projection 1 (i+0j+k).
How to find scalar projection and vector projection ?
We have been given two vectors <1 -1 1> and vector <1 0 1> , we are to find out the scalar and vector projection of vector <1 -1 1> onto vector <1 0 1>
We have vector a = <1 -1 1> and vector b = <1 0 1>
The scalar projection of vector a onto vector b means the magnitude of resolved component of vector a in the direction of vector b and is given by
The scalar projection of vector a onto vector b = [tex]\frac{vector b . vector a}{|vector b| }[/tex]
= [tex]\frac{(1-1+1)(1+0+1)}{\sqrt{1^{2} }+0+1^{2} }[/tex]
=[tex]\frac{1^{2} + 1^{2} }\sqrt{2}[/tex]
= [tex]\sqrt{2}[/tex]
The Vector projection of vector a onto vector b means the resolved component of vector a in the direction of vector b and is given by
The vector projection of vector a onto vector b .
= [tex]\frac{vector b . vector a}{| vector b|^{2} }[/tex] (i+0j+k)
= [tex]\frac{(1-1+1)(1+0+1)}{{1^{2} }+0+1^{2} }[/tex]. (i+0j+k)
= [tex]\frac{1^{2} + 1^{2} }{\sqrt{2} }[/tex] (i+0j+k)
= 1 (i+0j+k).
Thus from the above conclusion we can say that scalar projection scalar projection [tex]\sqrt{2}[/tex] and vector projection 1 (i+0j+k).
Learn more about the vector projection here: https://brainly.com/question/17477640
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