Question
If the foot of the perpendicular from the origin to a plane in $(a, b, c)$, the equation of the plane is(a) $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$(b) $a x+b y+c z=3$(c) $a x+b y+c z=a^{2}+b^{2}+c^{2}$(d) $a x+b y+c z=a+b+c$
Step 1
The foot of the perpendicular from the origin O(0, 0, 0) to the plane is P. Show more…
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If $z_{1}=2+i, z_{2}=-2+i 4$ and $\frac{1}{z_{3}}=\frac{1}{z_{2}}+\frac{1}{z_{2}}$, evaluate $z_{3}$ in the form $a+j b$. If $z_{1}, z_{2}, z_{3}$ are represented on an Argand diagram by the points $\mathrm{P}, \mathrm{Q}, \mathrm{R}$, respectively, prove that $R$ is the foot of the perpendicular from the origin on to the line $P Q$.
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Further problems
If $z_{1}=2+j, z_{2}=-2+j 4$ and $\frac{1}{z_{3}}=\frac{1}{z_{1}}+\frac{1}{z_{2}}$, evaluate $z_{3}$ in the form $a+j b$. If $z_{1}, z_{2}, z_{3}$ are represented on an Argand diagram by the points $\mathrm{P}, \mathrm{Q}, \mathrm{R}$, respectively, prove that $\mathrm{R}$ is the foot of the perpendicular from the origin on to the line PQ.
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