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Jenis sudut yang terbentuk antara vektor $(-1,2,2)$ dan $(2,1,0)$ adalah ... $\newline$ Select one: $\newline$ ( $1$ ) lancip $\newline$ siku-siku $\newline$ ( $1$ ) tumpul

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Sum of finite series not start from 1

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Q. Jenis sudut yang terbentuk antara vektor

(-1,2,2)

dan

(2,1,0)

adalah ...

\newline

Select one:

\newline

(

1

) lancip

\newline

siku-siku

\newline

(

1

) tumpul

Calculate dot product: Calculate the dot product of the vectors. $\newline$ $\vec{a} \cdot \vec{b} = (-1,2,2) \cdot (2,1,0) = (-1\times2) + (2\times1) + (2\times0)$ $\newline$ $= -2 + 2 + 0$ $\newline$ $= 0$
Determine vector magnitude: Determine the magnitude of each vector. $\newline$ $||(-1,2,2)|| = \sqrt{(-1)^2 + 2^2 + 2^2}$ $\newline$ $= \sqrt{1 + 4 + 4}$ $\newline$ $= \sqrt{9}$ $\newline$ $= 3$
Calculate second vector magnitude: Calculate the magnitude of the second vector. $\newline$ $||(2,1,0)|| = \sqrt{2^2 + 1^2 + 0^2}$ $\newline$ $= \sqrt{4 + 1 + 0}$ $\newline$ $= \sqrt{5}$
Find cosine of angle: Use the dot product and magnitudes to find the cosine of the angle. $\cos(\theta) = \frac{(-1,2,2) \cdot (2,1,0)}{\|(-1,2,2)\| \cdot \|(2,1,0)\|}$ $\cos(\theta) = \frac{0}{3 \cdot \sqrt{5}}$ $\cos(\theta) = 0$
Angle is right angle: Since the cosine of the angle is $0$ , the angle is a right angle.

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