सिद्ध कीजिए की रेखा `vec(r ) = 2hat(i) - 2hat(j) + 3hat(k) + t(hat(i) - hat(j) +4hat(k))` समतल `vec(r) . (hat(i) +5hat(j)+hat(k))=5` के समान्तर है उसके बीच की दूरी ज्ञात कीजिए।

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))

The lines vec(r)=hat(i)+t(5hat(i)+2hat(j)+hat(k)) and vec(r)=hat(i)+s(-10hat(i)-4hat(j)-2hat(k)) are -

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

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))