Related InterviewSolutions

• Find the length and the equations of the line of shortest distance between the lines `(x-8)/(3)=(y+9)/(-16) =(z-10)/(7) " and " (x-15)/(3)=(y-29)/(8)=(z-5)/(-5)`
• रेखाएँ, जिनकी सदिश समीकरण निम्नलिखित है, के बीच की न्यूनतम ज्ञात कीजिए : ` vecr = (1- t ) hati + ( t - 2) hatj + ( 3- 2t ) hatk ` और ` vec r = ( s + 1 ) hati + ( 2s - 1 ) hatj - ( 2s + 1 ) hatk `
• Find the Cartesian and vector equations of a line which passes through the point (1,2,3) and is parallel to the line . `(-x-2)/(1) =(y+3)/(7) =(2z-6)/(3)`
• Show that the lines `(x-1)/(2)=(y-2)/(3)=(z-3)/(4) " and " (x-4)/(5)=(y-1)/(2)=z` intersect each other . Find their point of intersection.
• Show that the lines `vec( r) =(hat(i) +hat(j) -hat(k)) +lambda (3hat(i) -hat(j)) " and " vec( r) =(4hat(i) -hat(k)) + mu (2hat(i) +3hat(k))` intersect . Find the point of the intersection.
• Show that the lines `(x+1)/(3)=(y+3)/(5) =(z+5)/(7) " and " (x-2)/(1)=(y-4)/(3)=(z-6)/(5)` intersect. Also find their point of intersection.
• Find the angle between the lines ` vec r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k)`and ` vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k)dot`
• Show that the lines `(x-1)/(3)=(y+1)/(2) =(z-1)/(5) " and " (x+2)/(4)=(y-1)/(3)=(z+1)/(-2)` do not intersect .
• Show that the lines `vec(r) =(hat(i) +2hat(j) +hat(k)) +lambda (hat(i)-hat(j)+hat(k)) " and " vec(r ) =(hat(i) +hat(j) -hat(k)) + mu (hat(i)- hat(j) + 2hat(k))` Do not intersect .
• Show that the lines ` vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k)`are coplanar. Also, find the plane containing these two lines.