TS EAMCET · Maths · Three Dimensional Geometry
The distance of the origin from the plane \(\mathbf{r} \cdot(3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-12 \hat{\mathbf{k}})=7\) measured parallel to the line \(\mathbf{r}=(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})+t(6 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})\) is
- A \(\frac{45}{8}\)
- B \(\frac{49}{10}\)
- C \(\frac{7}{10}\)
- D \(\frac{3}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{49}{10}\)
Step-by-step Solution
Detailed explanation
Since, equation of line passes through origin and parallel to the vector \((6 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})\) is \(\frac{x}{6}=\frac{y}{2}=\frac{z}{3}=r\) (Let) Now, a general point on the line (i) is \(P(6 r, 2 r, 3 r)\). Let point \(P(6 r, 2 r, 3 r)\)…
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