Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
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
#SPJ4
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
