The direction cosines to two lines at right angles are (1,2,3) and `(-2,1/2,1/3)` then the direction cosine prependicular to both the given lines are

Options

A. `sqrt((25)/(2198)),sqrt((38)/(1099)),sqrt((729)/(2198))`
B. `sqrt((24)/(2198)),sqrt((38)/(2198)),sqrt((730)/(2198))`
C. `1/3,-2,(-7)/2`
D. None of these

Answer

A

Explanation

Let the direction cosines of the line perpendicular to two given lines be (l,m,m).
`l+2m+3n=0" "[thereforel_1l_2+m_1m_2+n_1n_2=0]`
`and -2l+m/2+n/3=0`
On solving above equations, we get
`l/(2xx1/3-1/2xx3)=-m/(1xx1/3-3xx(-2))=n/(1xx1/2-2)=n/(1xx1/2-2(-2))`
`l^2/((25)/(36))=m^2/((361)/9)=n^2/((81)/4)=1/((25)/36+(361)/9+(81)/4)`
`therefore" "l=sqrt((25)/(2198)),m=sqrt((38)/(1099)),n=sqrt((729)/(2198))`