Find the equation of a line passing through the point (1,2,-4) and perpendicular to the lines r=(8i-19j+10k)+ lambda (3i-16j+7k) and - Maths - Vector Algebra

Question

Find the equation of a line passing through the point (1,2,-4) and
perpendicular to the lines r=(8i-19j+10k)+ lambda (3i-16j+7k) and
r=(15i+29j+5k)+mu(3i+8j-5k)

Saksham Tolani · Accepted Answer

Dear Student,

Let the line throught the point 1,2,-4 is r→=1i^+2j^-4k^+λ' ai^+bj^+ck^Line is perpendicular to the lines r→=8i^-19j^+10k^+a 3i^-16j^+7k^ and r→=15i^+29j^+5k^+a 3i^+8j^-5k^Vector perpendicular to both the line =i^j^k^3-16738-5=i^ 80-56- j^ -15-21+ k^ 24+48=24 i^ +36 j^ +72 k^So , equation of line isr→=1i^+2j^-4k^+λ' 24i^+36j^+72k^r→=1i^+2j^-4k^+12λ' 2i^+3j^+6k^r→=1i^+2j^-4k^+λ 2i^+3j^+6k^ ANS
     Say λ=12λ'

Regards!

Find the equation of a line passing through the point (1,2,-4) and perpendicular to the lines r=(8i-19j+10k)+ lambda (3i-16j+7k) and r=(15i+29j+5k)+mu(3i+8j-5k).