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Find the equation of the line which pas...

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector `3 hat i+2 hat j-2 hat k`.

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Given that the lines passes through the point `A(1,2,3)`. Therefore the position vector of A is `veca=hati+2hatj+3hatk` and line is parallel to ` vecb = 3hati+2hatj+2hatk`. Therefore, the equation of the line will be `vecr = veca + lambdavecb`, where `lambda` is constant.
`:. vecr = hati|2hatj|3hatk|lambda(3hati|2hatj-2hatk)`
Which is the required equation of the line.
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NAGEEN PRAKASHAN ENGLISH-THREE-DIMENSIONAL GEOMETRY -Exercise 11.2
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  2. Show that the line through the points (1, -1, 2) and (3, 4,-2) is p...

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  3. Show that the line through the points (4, 7, 8), (2, 3, 4)is parallel...

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  4. Find the equation of the line which passes through the point (1, 2, 3...

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  5. Find the equation of the line in vector and in cartesian form that ...

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  6. Find the Cartesian equation of the line which passes through the point...

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  7. The cartesian equation of a line is (x-5)/3=(y+4)/7=(z-6)/2. Write i...

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  8. Find the vector and the cartesian equations of the lines that passes ...

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  9. Find the vector and the cartesian equations of the line that passes t...

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  10. Find the angle between the following pairs of lines. (i) hatr = 2hat...

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  11. Find the angle between the following pair of lines: (x-2)/2=(y-1)/5=...

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  12. Find the values of p so that the lines (1-x)/3=(7y-14)/(2p)=(z-3)/2an...

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  13. Show that the lines (x-5)/7=(y+2)/(-5)=z/1and x/1=y/2=z/3are perpendi...

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  14. Find the shortest distance between the lines vecr=(hatii+2hatj+hatk)+l...

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  15. Find the shortest distance between the following lines: (x+1)/7=(y+1)...

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  16. Find the shortest distance vecr=hati+2hatj+3hatk+lambda(hati-3hatj+2ha...

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  17. Find the shortest distance between the lines whose vector equations a...

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