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Zina [86]
3 years ago
14

Find a unit vector that has the same direction as the given vector. 8i ? j + 4k

Mathematics
1 answer:
e-lub [12.9K]3 years ago
7 0

Answer with Step-by-step explanation:

a.Let given vector

a=8i-j+4k

\mid a\mid=\sqrt{(8)^2+(-1)^2+(4)^2}=9

By using the formula

Magnitude of a vector=\sqrt{x^2+y^2+z^2}

Where x=Coefficient of i

y=Coefficient of j

z=Coefficient of k

Unit vector=\hat{a}=\frac{a}{\mid a\mid}

By using the formula

The unit vector=\hat{a}=\frac{8i-j+4k}{9}=\frac{8}{9}i-\frac{1}{9}j+\frac{4}{9}k

b.Let vector b=-2i+4j+2k

\mid b\mid=\sqrt{(-2)^2+4^2+2^2}=2\sqrt 6

\hat{b}=\frac{-2i+4j+2k}{2\sqrt 6}

Length of vector=6

Therefore, the vector in the direction of <-2,4,2> with length 6 is given by =6\hat{b}=6\times \frac{-2i+4j+2k}{2\sqrt 6}

The vector in the direction of <-2,4,2> with length 6 is given by =-\sqrt 6(-i+2j+k)

c.\theta=\frac{\pi}{3}

\mid v\mid=8

Let v=v_x i+v_y j

v_x=\mid v\mid cos\theta

v_x=8cos\frac{\pi}{3}=8\times \frac{1}{2}=4

cos\frac{\pi}{3}=\frac{1}{2}

v_y=\mid v\mid sin\theta

v_y=8\times sin\frac{\pi}{3}=8\times \frac{\sqrt 3}{2}=4\sqrt 3

sin\frac{\pi}{3}=\frac{\sqrt 3}{2}

Therefore, the vector v in component form=4i+4\sqrt 3j

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A total of 259 tickets were sold to a benefit concert for a total of $5,312. Two types of tickets were sold: adult tickets were
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Step-by-step explanation:

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