# Find the acute angle between the lines whose direction ratios are 5, 12, -13 and 3, - 4, 5. - Mathematics and Statistics

Find the acute angle between the lines whose direction ratios are 5, 12, -13 and 3, - 4, 5.

#### Solution

cos theta=|(a_1a_2+b_1b_2+c_1c_2)/(sqrt(a_1^2+b_1^2+c_1^2)sqrt(a_2^2+b_2^2+c_2^2))|

=|(15-48-65)/(sqrt(25+144+169)sqrt(9+16+25))|

=|-98/(13sqrt2xx5sqrt2)|

=|-98/(13xx5xx2)|

=49/65

theta=cos^-1 (49/65)

Concept: Angle Between Two Lines
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