Question

The perpendicular distance from origin to the plane through the point (2, 3, –1) and perpendicular to vector is

• A. $\frac { 13 } { \sqrt { 74 } }$
• B. $- \frac { 13 } { \sqrt { 74 } }$
• C. 13
• D. None of these

Answer 1

Answer: (A)

$\frac { 13 } { \sqrt { 74 } }$

Answer 2

We know, the equation of the plane is

or $( r - ( 2 i + 3 j - k ) ) \cdot ( 3 i - 4 j + 7 k ) = 0$

⇒

⇒ $3 x - 4 y + 7 z + 13 = 0$

Hence, perpendicular distance of the plane from origin $= \frac { 13 } { \sqrt { 3 ^ { 2 } + ( - 4 ) ^ { 2 } + 7 ^ { 2 } } } = \frac { 13 } { \sqrt { 74 } }$