Question

If a, b, c are position vector of vertices of a triangle $ABC$, then unit vector perpendicular to its plane is

• A. $a \times b + b \times c + c \times a$
• B. $\frac{a \times b + b \times c + c \times a}{|a \times b + b \times c + c \times a|}$
• C. $\frac{a \times b}{|a \times b|}$
• D. None of these

Answer 1

Answer: (B)

$\frac{a \times b + b \times c + c \times a}{|a \times b + b \times c + c \times a|}$

Answer 2

Unit vector perpendicular to plane

$= \frac{\overset{\rightarrow}{AB} \times \overset{\rightarrow}{AC}}{|\overset{\rightarrow}{AB} \times \overset{\rightarrow}{AC}|} = \frac{(b - a) \times (c - a)}{\left| (b - a) \times (c - a) \right|}$

$= \frac{a \times b + b \times c + c \times a}{|a \times b + b \times c + c \times a|}.$