Find the distance of the point \left(\right. - 1 , - 5 , - 10 \left.\right) from the point of intersection of the line \overset{⃗}{r} = 2 \hat{i} - \hat{j} + 2 \hat{k} + \lambda \left(\right. 3 \hat{i} + 4 \hat{j} + 2 \hat{k} \left.\right) and plane \overset{⃗}{r} \cdot \left(\right. \hat{i}

Engineering

Mathematics

Line of Greatest Slope

Question

Find the distance of the point

(- 1, - 5, - 10)

from the point of intersection of the line

\vec{r} = 2 \hat{i} - \hat{j} + 2 \hat{k} + λ (3 \hat{i} + 4 \hat{j} + 2 \hat{k})

and plane

\vec{r} \cdot (\hat{i} - \hat{j} + \hat{k}) = 5

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