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Find the angle between the pairs of line...

Find the angle between the pairs of line `r=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) and hat(r)=5hat(i)-2hat(j)+mu(3hat(i)+2hat(j)+6hat(k))`.

Text Solution

Verified by Experts

The correct Answer is:
`cos^(-1)((19)/(21))`
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Find the angle between the pair of lines r=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) r=5hat(i)-4hat(k)+mu(3hat(i)+2hat(j)+6hat(k))

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Find the angle between the pair of line vec(r)=2hat(i)-5hat(j)+hat(k)+lamda(3hat(i)+2hat(j)+6hat(k)) and vec(r)=7hat(i)-6hat(k)+mu(hat(i)+2hat(j)+2hat(k)) .

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Find the angle between the pairs of lines vec(r)=3hat(i)+hat(j)-2hat(k)+lamda(hat(i)-hat(j)-2hat(k)) vec(r)=2hat(i)-hat(j)-56hat(k)+mu(3hat(i)-5hat(j)-4hat(k))

Find the angle between the pair of lines vec(r)=2hat(i)-5hat(j)+hat(k)+lamda(3hat(i)+2hat(j)+6hat(k)) and vec(r)=7hat(i)-6hat(k)+hat(h)(hat(i)+2hat(j)+2hat(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))

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

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

Find the shortest distance between the line vec(r)=hat(i)-7hat(j)-2hat(k)+lamda(hat(i)+3hat(j)+2hat(k)) and vec(r)=3hat(i)+4hat(j)-2hat(k)+mu(-hat(i)+2hat(j)+hat(k)) .

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