Find the scalar magnitude of the projection of 2 i-3 j+4 k on i-j Express as a Cartesian vector: vec{a}=(2,-3,4) quad and quad vec{b}=(1,-1,0)

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Accepted Answer

Step:1 ：Find the dot product of the two vectors: (vec{a} cdot vec{b} = (2)(1) + (-3)(-1) + (4)(0) = 5)Step:2 ：Find the magnitude of vector (vec{b}): (||vec{b}|| = sqrt{(1)^2 + (-1)^2 + (0)^2} = sqrt{2})Step:3 ：Calculate the scalar magnitude of the projection: (frac{vec{a} cdot vec{b}}{||vec{b}||} = frac{5}{sqrt{2}} = frac{5sqrt{2}}{2})Step:4 ：(boxed{text{Final Answer: }frac{5sqrt{2}}{2}})

Answer

Step: 1 ：Find the dot product of the two vectors: (vec{a} cdot vec{b} = (2)(1) + (-3)(-1) + (4)(0) = 5)Step: 2 ：Find the magnitude of vector (vec{b}): (||vec{b}|| = sqrt{(1)^2 + (-1)^2 + (0)^2} = sqrt{2})Step: 3 ：Calculate the scalar magnitude of the projection: (frac{vec{a} cdot vec{b}}{||vec{b}||} = frac{5}{sqrt{2}} = frac{5sqrt{2}}{2})Step: 4 ：(boxed{text{Final Answer: }frac{5sqrt{2}}{2}})

Find the scalar magnitude of the projection of $2 i-3 j+4 k$ on $i-j$ Express as a Cartesian vector: $\vec{a}=(2,-3,4) \quad$ and $\quad \vec{b}=(1,-1,0)$

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