What is the unit vector that is orthogonal to the plane containing # ( i - 2 j + 3 k) # and # ( - 5 i + 4 j - 5 k) #?

1 Answer
Jun 29, 2016

Answer:

#= 1/sqrt(35)<1,5,3>#

Explanation:

you need to calculate the vector (cross) product of these two vectors to get the normal vector

it's not clear to me how you latex matrices on here so i will draw the computation.

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so the normal vector is the determinant of the matrix as shown and we get as one possible normal vector [there an an infinite number of actual formulations of this]

#vec n = <1,5,3>#

the unit vector is therefore

#hat n = 1/sqrt(1^2 + 5^2 + 3^3)<1,5,3>#

#= 1/sqrt(35)<1,5,3>#

or

#= - 1/sqrt(35)<1,5,3># pointing in other direction