What is the angle between the vector r=(4i^+8j^+k^ ) and the x-axis?

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What is the angle between the vector { r } =(4 { i } +8 { j

Question

What is the angle between the vector $r = (4 \hat{i} + 8 \hat{j} + \hat{k})$ and the x-axis?

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What is the angle between the vector

r = (4 \hat{i} + 8 \hat{j} + \hat{k})

and the x-axis?

14 mins ago

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Text solutionVerified

We know that if

a, b

and

c

are the direction ratios, then the direction cosines

l, m

and

n

are given by

Direction cosines are

l = \frac{a}{a 2 + b 2 + c 2}, m = \frac{b}{a 2 + b 2 + c 2}, n = \frac{c}{a 2 + b 2 + c 2},

And, If

α, β,

and

γ

are the angles made by the line segment with the coordinate axis.

cos α, cos β

and

cos γ

are called as the direction cosines and are usually denoted by

l, m

and

n .

l = cos α, m = cos β

and

n = cos γ

Direction ratios of the given vector are

4, 8, 1

and

(4)^{2} + (8)^{2} + (1)^{2} = 81 = 9

Direction cosines of the given vector are

\frac{4}{9}, \frac{8}{9}, \frac{1}{9}

Let

α

be the angle between the given vectors and x-axis

Then

cos α = \frac{4}{9}

\Rightarrow

α = cos^{- 1} (\frac{4}{9})

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Question Text	What is the angle between the vector $r = (4 \hat{i} + 8 \hat{j} + \hat{k})$ and the x-axis?
Answer Type	Text solution:1
Upvotes	150

What is the angle between the vector r=(4i^+8j^​+k^ ) and the x-axis?

Text solutionVerified

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