Question

The perpendicular distance of A(1, 4, -2) from BC is, where B = (2, 1, -2) and C = (0, -5, 1)

• A. $\frac{\sqrt{26}}{7}$
• B. $\frac{2\sqrt{26}}{7}$
• C. $\frac{3\sqrt{26}}{7}$
• D. $\frac{4\sqrt{26}}{7}$

Answer 1

The correct option is B $\frac{2\sqrt{26}}{7}$



$AD=AB.sin\theta$

$=AB.\frac{|\overline{BC}\times \overline{BA}|}{|\overline{BC}||\overline{BA}|}=\frac{|\overline{BC}\times \overline{BA}|}{|\overline{BC}|}$

$=\frac{|(-2i-6j+3k)\times (-i+3j)|}{\sqrt{4+36+9}}=\frac{2\sqrt{26}}{7}$