Find the measure of a acute angle between the line direction ratios are 5, 12, -13 and 3, -4, 5.

Explanation

`a_(1)=5, b_(1)=12, c_(1)=-13`
`a_(2)=3, b_(2)=-4, c_(2)=5`
Acute angle, `cos theta=|(a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2))/(sqrt(a_(1)^(2)+b_(1)^(2)+c_(1)^(2))sqrt(a_(2)^(2)+b_(2)^(2)+c_(2)^(2)))|`
`rArr" "cos theta=|(15-48-65)/(sqrt(25+144+169)sqrt(9+16+25))|`
`rArr" "cos theta=|(-98)/(13sqrt2xx5xxsqrt2)|`
`rArr" "cos theta=|(-98)/(13xx5xx2)|`
`rArr" "cos theta =|-(49)/(65)|`
`rArr" "cos theta =(49)/(65)`
`therefore" "theta=cos^(-1)((49)/(65))`