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find-dc-s-dr-s-of-a-mormal-to-the-plane-2x-5-2-y-7-8-z-23-




Question Number 9453 by Raja Naik last updated on 09/Dec/16
find dc′s dr′s of a mormal to the   plane 2x+(5/2)y+(7/8)z=23
$$\mathrm{find}\:\mathrm{dc}'\mathrm{s}\:\mathrm{dr}'\mathrm{s}\:\mathrm{of}\:\mathrm{a}\:\mathrm{mormal}\:\mathrm{to}\:\mathrm{the}\: \\ $$$$\mathrm{plane}\:\mathrm{2x}+\frac{\mathrm{5}}{\mathrm{2}}\mathrm{y}+\frac{\mathrm{7}}{\mathrm{8}}\mathrm{z}=\mathrm{23} \\ $$
Answered by mrW last updated on 10/Dec/16
d.r.′s of the normal are (2,(5/2),(7/8))  (√(2^2 +((5/2))^2 +((7/8))^2 ))=((√(705))/8)  2×(8/( (√(705))))=((16)/( (√(705))))  (5/2)×(8/( (√(705))))=((20)/( (√(705))))  (7/8)×(8/( (√(705))))=(7/( (√(705))))  d.c.′s of the normal are (((16)/( (√(705)))),((20)/( (√(705)))),(7/( (√(705)))))
$$\mathrm{d}.\mathrm{r}.'\mathrm{s}\:\mathrm{of}\:\mathrm{the}\:\mathrm{normal}\:\mathrm{are}\:\left(\mathrm{2},\frac{\mathrm{5}}{\mathrm{2}},\frac{\mathrm{7}}{\mathrm{8}}\right) \\ $$$$\sqrt{\mathrm{2}^{\mathrm{2}} +\left(\frac{\mathrm{5}}{\mathrm{2}}\right)^{\mathrm{2}} +\left(\frac{\mathrm{7}}{\mathrm{8}}\right)^{\mathrm{2}} }=\frac{\sqrt{\mathrm{705}}}{\mathrm{8}} \\ $$$$\mathrm{2}×\frac{\mathrm{8}}{\:\sqrt{\mathrm{705}}}=\frac{\mathrm{16}}{\:\sqrt{\mathrm{705}}} \\ $$$$\frac{\mathrm{5}}{\mathrm{2}}×\frac{\mathrm{8}}{\:\sqrt{\mathrm{705}}}=\frac{\mathrm{20}}{\:\sqrt{\mathrm{705}}} \\ $$$$\frac{\mathrm{7}}{\mathrm{8}}×\frac{\mathrm{8}}{\:\sqrt{\mathrm{705}}}=\frac{\mathrm{7}}{\:\sqrt{\mathrm{705}}} \\ $$$$\mathrm{d}.\mathrm{c}.'\mathrm{s}\:\mathrm{of}\:\mathrm{the}\:\mathrm{normal}\:\mathrm{are}\:\left(\frac{\mathrm{16}}{\:\sqrt{\mathrm{705}}},\frac{\mathrm{20}}{\:\sqrt{\mathrm{705}}},\frac{\mathrm{7}}{\:\sqrt{\mathrm{705}}}\right) \\ $$

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