Question

Find both the scalar projection compvuand the vector projection projvuof the vectoru=〈1,−1,1〉onto the vectorv=〈1,0,1〉. answer:. . . . . . . . . . . . . . . . . . . .

Answer 1

Its Scalar projection $\sqrt{2}$ 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 = $\frac{vector b . vector a}{|vector b| }$

                                                                             = $\frac{(1-1+1)(1+0+1)}{\sqrt{1^{2} }+0+1^{2} }$

                                                                             =$\frac{1^{2} + 1^{2} }\sqrt{2}$

                                                                             = $\sqrt{2}$

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 .

                                    = $\frac{vector b . vector a}{| vector b|^{2} }$ (i+0j+k)

                                   = $\frac{(1-1+1)(1+0+1)}{{1^{2} }+0+1^{2} }$. (i+0j+k)

                                   =  $\frac{1^{2} + 1^{2} }{\sqrt{2} }$ (i+0j+k)

                                   = 1 (i+0j+k).

Thus from the above conclusion we can say that scalar projection scalar projection $\sqrt{2}$ and vector projection 1 (i+0j+k).  

Learn more about the vector projection here: brainly.com/question/17477640

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