Q92 / 150 · MHT CET 2017 · Mathematics

The equation of the plane through $(- 1, 1, 2),$ whose normal makes equal acute angle with co-ordinate axes is

Correct answer
A
$\vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 2$
B
$\vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 6$
C
$\vec{r} \cdot (3 \hat{i} - 3 \hat{j} + 3 \hat{k}) = 2$
D
$\vec{r} . (\hat{i} + \hat{j} + \hat{k}) = 3$

Solution

Equation plane passing through

A (\vec{a})

and

⊥

to

\vec{n}

is

\vec{r} . \vec{n} = \vec{a} . \vec{n}

Here

\vec{a} = - \hat{i} + \hat{j} + 2 \hat{k}, \vec{n} = \hat{i} + \hat{j} + \hat{k}

∴ \vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = (- \hat{i} + \hat{j} + 2 \hat{k}) . (\hat{i} + \hat{j} + \hat{k}) = 2

Hence, the correct answer is option: 'A'.

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