From fig

\(\displaystyle{O}{B}={1}{i}+{1.5}{k}\)

\(\displaystyle{O}{G}={1.85}{j}+{0.7}{k}\)

\(\displaystyle{B}{G}={O}{G}-{O}{B}=-{i}+{1.85}{j}-{0.8}{k}\)

\(\displaystyle{\left|{B}{G}\right|}=\sqrt{{{1}^{{2}}+{1.85}^{{2}}+{0.8}^{{2}}}}={2.25}\)

\(\displaystyle\lambda={\frac{{{B}{G}}}{{{\left|{B}{G}\right|}}}}={\frac{{-{i}+{1.85}{j}-{0.8}{k}}}{{{2.25}}}}\)

\(\displaystyle\vec{{{F}}}={F}\times\lambda\)

Where F=450 N

Find \(\displaystyle\vec{{{F}}}\)

But, \(\displaystyle\vec{{{F}}}={F}_{\xi}+{F}_{{y}}{j}+{F}_{{z}}{k}\)

\(\displaystyle\vec{{{F}}}={450}\times{\left({\frac{{-{i}+{1.85}{j}-{0.8}{k}}}{{{2.25}}}}\right)}\)

\(\displaystyle=-{200}{i}+{370}{j}-{160}{k}\)

\(\displaystyle{F}_{{x}}=-{200}\) N

\(\displaystyle{F}_{{y}}={370}\) N

\(\displaystyle{F}_{{z}}=-{160}\) N

\(\displaystyle{O}{B}={1}{i}+{1.5}{k}\)

\(\displaystyle{O}{G}={1.85}{j}+{0.7}{k}\)

\(\displaystyle{B}{G}={O}{G}-{O}{B}=-{i}+{1.85}{j}-{0.8}{k}\)

\(\displaystyle{\left|{B}{G}\right|}=\sqrt{{{1}^{{2}}+{1.85}^{{2}}+{0.8}^{{2}}}}={2.25}\)

\(\displaystyle\lambda={\frac{{{B}{G}}}{{{\left|{B}{G}\right|}}}}={\frac{{-{i}+{1.85}{j}-{0.8}{k}}}{{{2.25}}}}\)

\(\displaystyle\vec{{{F}}}={F}\times\lambda\)

Where F=450 N

Find \(\displaystyle\vec{{{F}}}\)

But, \(\displaystyle\vec{{{F}}}={F}_{\xi}+{F}_{{y}}{j}+{F}_{{z}}{k}\)

\(\displaystyle\vec{{{F}}}={450}\times{\left({\frac{{-{i}+{1.85}{j}-{0.8}{k}}}{{{2.25}}}}\right)}\)

\(\displaystyle=-{200}{i}+{370}{j}-{160}{k}\)

\(\displaystyle{F}_{{x}}=-{200}\) N

\(\displaystyle{F}_{{y}}={370}\) N

\(\displaystyle{F}_{{z}}=-{160}\) N