Find-the-angle-between-the-line-x-2-3-y-1-1-z-3-2-and-the-plane-3x-4y-z-5-0-

Question Number 132904 by bramlexs22 last updated on 17/Feb/21

Find the angle between the line

\frac{x - 2}{3} = \frac{y + 1}{- 1} = \frac{z - 3}{2} and the

plane 3 x + 4 y + z + 5 = 0

Answered by mr W last updated on 17/Feb/21

l : (3, - 1, 2)

n : (3, 4, 1)

ϕ = 90 ° - θ

= 90 ° - \cos^{- 1} \frac{l \cdot n}{∣ l ∣∣ n ∣}

= \sin^{- 1} \frac{l \cdot n}{∣ l ∣∣ n ∣}

= \sin^{- 1} \frac{(9 - 4 + 2)}{\sqrt{(9 + 1 + 4) (9 + 16 + 1)}}

= 21.525 °

Commented by liberty last updated on 17/Feb/21

why n : (3, 4, 5) ? it should (3, 4, 1)

Commented by mr W last updated on 17/Feb/21

{i t}^{'} s m i s r e a d . t h a n k s f o r p o i n t i n g o u t!

Commented by mr W last updated on 17/Feb/21

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