What is the unit vector that is orthogonal to the plane containing $<3, -6, 2>$ and $<3, 2, 1>$ ?

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What is the unit vector that is orthogonal to the plane containing $<3, -6, 2>$ and $<3, 2, 1>$ ?

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Answer 1 · 2016-02-21T15:17:48

$(-10/sqrt 685*i+3/sqrt 685*j+24/sqrt 685.k)$

Explanation:

$"step 1:Find cross product of two vector"$
$"the cross product of two vector in the same plane is perpendicular to the plane"$
$"let "vec C=vec A X vec B$
$vec C=i(a_y*b_z-a_z*b_y)-j(a_x*b_z-a_z*b_x)+k(a_x*b_y-a_y*b_x)$
$vec c=i(-10)-j(-3)+k(24)$
$vec C=-10i+3j+24k$
$"step 2:Find magnitude of the vector of " vec C$
$||c||=sqrt((-10)^2+3^2+24^2)$
$||c||=sqrt (100+9+576)$
$||c||=sqrt 685$
$step 3:" use : vec C /||c||$
$(-10i+3j+24k)/sqrt 685$
$(-10/sqrt 685*i+3/sqrt 685*j+24/sqrt 685.k)$

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What is the unit vector that is orthogonal to the plane containing $<3, -6, 2>$ and $<3, 2, 1>$ ?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

What is the unit vector that is orthogonal to the plane containing <3, -6, 2> <3, -6, 2> and <3, 2, 1> <3, 2, 1> ?

1 Answer

Explanation:

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What is the unit vector that is orthogonal to the plane containing $<3, -6, 2>$ and $<3, 2, 1>$ ?