Q.27. The equation of the plane through (-1, 1, 2) whose normal makes equal acute angles with coordinate axes is
A. x + y + z – 3 = 0
B. x + y + z – 2 = 0
C. x + y – z – 2 = 0
D. x – y + z – 3 = 0
Answer: B. x+y+z-2 = 0
Explanation :-
Note that (-1, 1, 2) is satisfied by only option (B).
Alternate Method:
Let A ≡ (-1, 1, 2)
\overrightarrow{n}=-\hat{i}+\hat{j}+2\hat{k} {\vec{n}}=\hat{i}+\hat{j}+\hat{k}Equation of plane is \vec{r}⋅\vec{n}=\vec{a}⋅\vec{n}
⇒ \vec{r}⋅(\hat{i}+\hat{j}+\hat{k})=(-\hat{i}+\hat{j}+2\hat{k})⋅(\hat{i}+\hat{j}+\hat{k})
⇒ \vec{r}⋅(\hat{i}+\hat{j}+\hat{k})=2
⇒ (x\hat{i}+y\hat{j}+z\hat{k})⋅(\hat{i}+\hat{j}+\hat{k})=2
⇒ x+y+z-2=0