Question

The acute angle between the line joining the points (2,1,-3) and (-3,1,7)and a line parallel to `(x-1)/3=y/4=(z+3)/5` through the point (-1,0,4) is
A. `cos^(-1)((1)/(sqrt(10)))`
B. `cos^(-1)((1)/(5sqrt(10)))`
C. `cos^(-1)((7)/(5sqrt(10)))`
D. `cos^(-1)((3)/(5sqrt(10)))`

Answer 1

Correct Answer - C
Direction ratio of the line joining the points (2,1,-3) and (-3,1,7) are `(a_(1),b_1,c_(1))i.e, (-5,0,10)`
Direction ratio of the line parallel to line `(x-1)/(3)=(y)/(4)=(z+3)/(5)"are"(a_(2),b_(2),c_(2))i.e, (3,4,5)`
Angle between two lines is given by
`cos theta=((-5xx3)+(0xx4)+(10xx5))/(sqrt(25+0+100)sqrt(9+16+25))=(35)/(25sqrt10)`
`therefore theta=cos^(-1)((7)/(5sqrt10))`