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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))`.

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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))

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)) .

BETTER CHOICE PUBLICATION-THREE DIMENSIONAL GEOMETRY -ASSIGNMENT MOST IMPORTANT QUESTIONS FOR PRACTICE (SECTION IV) Short Answer Type Questions
  1. Find the angle between the pairs of line r=3hat(i)+2hat(j)-4hat(k)+lam...

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  2. Find the angle between the following lines vec(r)=3hat(i)+hat(j)-2ha...

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  3. Find the angle between the following lines (x+1)/(1)=(y-4)/(1)=(z-5)...

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  4. Find the angle between the following lines (x-5)/(1)=(2y+6)/(-2)=(z-...

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  5. Find the angle between the following lines (5-x)/(3)=(y+3)/(-2),z=5 ...

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  6. Find the angle between the pairs of line with direction ratios lt5,-...

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  7. Find the angle between the lines whose direction ratios are a, b, c an...

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  8. Show that the following lines are perpendicular (x-3)/(2)=(y+1)/(-3...

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  9. Show that the following lines are perpendicular (-x+2)/(-2)=(y-1)/(...

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  10. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(2) and (x-1)/(3k)=(y-1)/(1)=...

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  11. Find the value of lamda of the following pair of lines are perpendicul...

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  12. Find the value of lamda of the following pair of lines are perpendicul...

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  13. Find the value of lamda of the following pair of lines are perpendicul...

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  14. The angle between the lines whose direction cosines are given by the ...

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  15. If a line makes angles 30°,60° and 90° with x,y and z-axis respectivel...

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  16. Find the angle between the two lines whose direction cosines are given...

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  17. Find the equation of a line passing through the point P(2,-1,-3) and p...

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  18. Find the vector and cartesian equation of the line passing through the...

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