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If the shortest distance between the lines `vec(r_(1))=alphahat(i)+2hat(j)+2hat(k)+lambda(hat(i)-2hat(j)-2hat(k)),lambdainR,alpha gt 0 and vec(r_(2)) = - 4hat(i) - hat(k) + mu (3hat(i)-2hat(j)-2hat(k)),mu in R` is 9, then `alpha` is equal to ________ .

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Find the shortest distance between the lines : vec(r) = (4hat(i) - hat(j)) + lambda(hat(i) + 2hat(j) - 3hat(k)) and vec(r) = (hat(i) - hat(j) + 2hat(k)) + mu (2hat(i) + 4hat(j) - 5hat(k))

Find the shortest distance between the lines L_(1) " and " L_(2) given by vec( r )=hat(i) +hat(j) +lambda(2hat(i)-hat(j)+hat(k)) " and " vec(r )=2hat(i) +hat(j)-hat(k) +mu (4hat(i) -2hat(j) +2hat(k))

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 .

vec(r ) =(3hat(i) +hat(j)-2hat(k)) +lambda (hat(i)-hat(j)-2hat(k)) " and " vec(r ) =(2hat(i) -hat(j) -5hat(k)) + mu (3hat(i) -5hat(j) -4hat(k)) FInd angle between the lines

vec(r )=(-4hat(i)+4hat(j) +hat(k)) + lambda (hat(i) +hat(j) -hat(k)) vec(r)=(-3hat(i) -8hat(j) -3hat(k)) + mu (2hat(i) +3hat(j) +3hat(k))

Show that the lines vec(r )=(3hat(i) -15hat(j) + 9hat(k)) + lambda(2hat(i) -7hat(j) +5hat(k)) and vec(r )=(-hat(i) + hat(j) + 9hat(k)) + mu (2hat(i) + hat(j) -3hat(k)) do not intersect.

vec(r ) =(hat(i) +2hat(j) +3hat(k)) + lambda(hat(i) -3hat(j) +2hat(k)) vec(r ) =(4hat(i) +5hat(j) +6hat(k)) + mu (2hat(i) + hat(j) +2hat(k)) Find the the shortest between the lines

JEE MAINS PREVIOUS YEAR-JEE MAINS 2021-MATHEMATICS (SECTION -B)
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