Question

The vector equation of plane containing the point (1, -1, 2) and perpendicular to planes 2x+3y-2z=5 and x+2y-3z = 8 is

• A. $\overrightarrow{r} \cdot (-5i+4j-k) = -7$
• B. $\overrightarrow{r} \cdot (-5i+4j-k) = 7$
• C. $\overrightarrow{r} \cdot (-5i+4j+k) = -7$
• D. $\overrightarrow{r} \cdot (-5i+4j+k) = 7$

Answer 1

Answer: (C)

$\overrightarrow{r} \cdot (-5i+4j+k) = -7$

Answer 2

Plane Equation:

• Normals of given planes: n₁ = (2,3,–2), n₂ = (1,2,–3).
• Required plane’s normal = n₁ × n₂ = (–5, 4, 1).
• Using point (1,–1,2): (–5)(1)+4(–1)+1(2)= –7.
• Equation: $\overrightarrow{r} \cdot (-5i+4j+k)= –7$