Maharashtra State BoardHSC Arts 12th Board Exam
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The Measure of Acute Angle Between the Lines Whose Direction Ratios Are 3, 2, 6 and –2, 1, 2 is ______. - Mathematics and Statistics

The measure of the acute angle between the lines whose direction ratios are 3, 2, 6 and –2, 1, 2 is ______.

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Solution

`cos theta = |(3xx-2+2xx1+6xx2)/(sqrt((3)^2+(2)^2+(6)^2)sqrt((-2)^2+1^2 +2^2))|`

=`|(-6+2+12)/(sqrt49sqrt9)| = 8/(7xx3) = 8/21`

`=> theta = cos^(-1) (8/21)`

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