The angle between planes 2x+3y-z=5 and x-y+2z=3 satisfies cos(theta) =

|-3| / (sqrt(14)*sqrt(6)), using only the absolute value

3 / (sqrt(14)*sqrt(6)), dropping the negative sign

(2-3-2) / (sqrt(14)*sqrt(6)), an unsimplified numerator

The angle between planes 2x+3y-z=5 and x-y+2z=3 satisfies…

Answer: All three expressions are equivalent.

A |-3| / (sqrt(14)*sqrt(6)), using only the absolute value
B 3 / (sqrt(14)*sqrt(6)), dropping the negative sign
C (2-3-2) / (sqrt(14)*sqrt(6)), an unsimplified numerator
D All three expressions are equivalent

Correct answer: D. All three expressions are equivalent

Explanation: n₁=(2,3,-1), n₂=(1,-1,2). n₁.n₂=2-3-2=-3. |n₁|=sqrt(14), |n₂|=sqrt(6). cos(theta)=|n₁.n₂|/(|n₁||n₂|) = |-3|/sqrt(84) = 3/sqrt(84). Options A, B, C all equal the same value.

Three mutually perpendicular axes x, y, z meeting at the origin O, with a point P located by its (x, y, z) coordinates.

Concept context

Lines and planes in 3D space, direction cosines, distances, and angles

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The angle between planes 2x+3y-z=5 and x-y+2z=3 satisfies cos(theta) =

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