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Question

# For every point P (x, y, z) on the x-axis (except the origin), (a) x = 0, y = 0, z ≠ 0 (b) x = 0, z = 0, y ≠ 0 (c) y = 0, z = 0, x ≠ 0 (d) x = y = z = 0

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Solution

## $\left(\mathrm{c}\right)y=0\mathit{,}\mathit{}z\mathit{}=0\mathit{,}\mathit{}x\mathit{}\ne 0\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Both}Y\mathit{}\mathrm{and}Z\mathrm{coordinates}\mathrm{on}\mathrm{each}\mathrm{point}\mathrm{of}\mathit{}\mathrm{the}x-\mathrm{axis}\mathrm{are}\mathrm{equal}\mathrm{to}\mathrm{zero}.\mathrm{The}X-\mathrm{coordinate}\mathrm{on}\mathrm{the}\mathrm{origin}\mathrm{is}\mathrm{also}\mathrm{equal}\mathrm{to}\mathrm{zero}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},\mathrm{the}Y\mathit{}\mathrm{and}Z\mathrm{coordinates}\mathrm{on}\mathrm{each}\mathrm{point}\mathrm{of}\mathit{}\mathrm{the}x-\mathrm{axis},\mathrm{except}\mathrm{the}\mathrm{origin},\mathrm{are}\mathrm{equal}\mathrm{to}\mathrm{zero},\mathrm{while}\mathrm{the}X-\mathrm{coordinate}\mathrm{is}\mathrm{non}-\mathrm{zero}.\phantom{\rule{0ex}{0ex}}$

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