If a, b, c are the \[{{p}^{th}},\text{ }{{q}^{th}}.\text{ }{{\text{r}}^{th}}\] terms of an HP and \[\vec{u}=(q-r)\vec{i}+(r-p)\vec{j}+(p-q)\vec{k},\vec{v}=\frac{{\vec{i}}}{a}+\frac{{\vec{j}}}{b}+\frac{{\vec{k}}}{c}\] then

\[\vec{u},\vec{v}\] are parallel vectors

\[\vec{u},\vec{v}\] are orthogonal vectors

\[\vec{u}\times \vec{v}=\vec{i}+\vec{j}+\vec{k}\]

If a, b, c are the \[{{p}^{th}},\text{ }{{q}^{th}}.\text{ }{{\text{r}}

1.	If a, b, c are the \[{{p}^{th}},\text{ }{{q}^{th}}.\text{ }{{\text{r}}^{th}}\] terms of an HP and \[\vec{u}=(q-r)\vec{i}+(r-p)\vec{j}+(p-q)\vec{k},\vec{v}=\frac{{\vec{i}}}{a}+\frac{{\vec{j}}}{b}+\frac{{\vec{k}}}{c}\] then
A.	\[\vec{u},\vec{v}\] are parallel vectors
B.	\[\vec{u},\vec{v}\] are orthogonal vectors
C.	\[\vec{u}.\vec{v}=1\]
D.	\[\vec{u}\times \vec{v}=\vec{i}+\vec{j}+\vec{k}\]
Answer» C. \[\vec{u}.\vec{v}=1\]

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If a, b, c are the \[{{p}^{th}},\text{ }{{q}^{th}}.\text{ }{{\text{r}}^{th}}\] terms of an HP and \[\vec{u}=(q-r)\vec{i}+(r-p)\vec{j}+(p-q)\vec{k},\vec{v}=\frac{{\vec{i}}}{a}+\frac{{\vec{j}}}{b}+\frac{{\vec{k}}}{c}\] then

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