We want to find the equation of the line passing through the origin that makes an angle of arctan=1/2 with the line 3y=2x:
The slope of the given line is 2/3, and the given line also passes through the origin.
The angle between the lines is related by the following:
`tan theta = (m_1-m_2)/(1+m_1m_2) `
Since the angle is arctan (1/2), we know that `tan theta = 1/2 `
Then ` 1/2=(m-2/3)/(1+m*2/3) ` where m...
We want to find the equation of the line passing through the origin that makes an angle of arctan=1/2 with the line 3y=2x:
The slope of the given line is 2/3, and the given line also passes through the origin.
The angle between the lines is related by the following:
`tan theta = (m_1-m_2)/(1+m_1m_2) `
Since the angle is arctan (1/2), we know that `tan theta = 1/2 `
Then ` 1/2=(m-2/3)/(1+m*2/3) ` where m is the slope of the required line.
So `1/2+1/3m=m-2/3 `
`2/3 m = 7/6 ==> m=7/4 `
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The equation is y=7/4x or 4y=7x
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The given line and the required line:
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