Consider the following 3lines in space
`L_1:r=3hat(i)-hat(j)+hat(k)+lambda(2hat(i)+4hat(j)-hat(k))`
`L_2: r=hat(i)+hat(j)-3hat(k)+mu(4hat(i)+2hat(j)+4hat(k))`
`L_3:=3hat(i)+2hat(j)-2hat(k)+t(2hat(i)+hat(j)+2hat(k))`
Then, which one of the following part(s) is/ are in the same plane?

Consider the following 3 lines in space L_1: vec r= 3hat i-hat j+ 2hat k + lambda(2hat i + 4hat j-hat k) , L_2 :vec r =hat i+hat j- 3hat k + mu(4hat i + 2hat j+ 4hat k) and L_3 : vec r = 3hat i+2hat j- 2hat k + t(2hat i+hat j+ 2hat k) Then which one of the following pair(s) are in the same plane.

If 3hat(i) + 2hat(j) -5hat(k)= x(2hat(i) -hat(j) + hat(k)) + y(hat(i) + 3hat(j)-2hat(k))+z(-2hat(i) + hat(j)-3hat(k)) , then

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))

Find the shortest distance between the following lines vec(r)=hat(i)-hat(j)-hat(k)+lamda(hat(i)+hat(j)-hat(k)) and vec(r)=3hat(i)-hat(j)-2hat(k)+mu(-hat(i)+2hat(j)+hat(k))

If [[hat(i)+4hat(j)+6hat(k), 2hat(i)+ahat(j)+3hat(k), hat(i)+2hat(j)-3hat(k)]]=0 then a=

Find the shortest distance between the lines. r=(hat(i)+2hat(j)+hat(k))+lambda(hat(i)-hat(j)+hat(k)) " and " r=(2hat(i)-hat(j)-hat(k))+mu(2hat(i)+hat(j)+2hat(k)) .