Question

Unit vector perpendicular to the plane of the triangle ABC with position vectors `veca, vecb, vecc` of the vertices A, B, C is ______.

Options

• `((veca xx vecb + vecb xx vecc + vecc xx veca))/Δ`

• `((veca xx vecb + vecb xx vecc + vecc xx veca))/(2Δ)`

• `((veca xx vecb + vecb xx vecc + vecc xx veca))/(4Δ)`

• `(2(veca xx vecb + vecb xx vecc + vecc xx veca))/Δ`

Answer 1

Unit vector perpendicular to the plane of the triangle ABC with position vectors `veca, vecb, vecc` of the vertices A, B, C is `underlinebb(((veca xx vecb + vecb xx vecc + vecc xx veca))/(2Δ))`.

Explanation:

= `((veca - vecb) xx (veca - vecc))/|(veca - vecb) xx (veca - vecc)|`

= `((veca - vecb) xx (veca - vecc))/(2Δ)`

= `(-veca xx vecc - vecb xx veca + vecb xx vecc)/(2Δ)`

= `(veca xx vecb + vecb xx vecc + vecc xx veca)/(2Δ)`