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Find the Cartesian equation of a line which passes through the point having position vector `(2hat(i) -hat(j) + 4hat(k)) ` and is in the direction of the vector ,`(hat(i) +2hat(j) -hat(k))`

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The correct Answer is:
`(x-2)/(1)=(y+1)/(2)=(z-4)/(-1)`
The required line passes through the point (2,-1,4) and it has direction ratios 1,2,-1
`:. ` its equations in `(x-2)/(1)=(y+1)/(2)=(z-4)/(-1)`
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RS AGGARWAL-STRAIGHT LINE IN SPACE-Exercise 27F
  1. Write the equations of a line parallel to the line (x-2)/(-3) =(y+3...

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  2. Find the Cartesian equations of the line which passes through ...

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  3. Write the vector equation of a line whose Cartesian equations a...

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  4. The Cartesian equations of a line are (3-x)/(5) =(y+4)/(7) =(2z-6)/...

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  5. Write the vector equation of a line passing through the point (...

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  6. If P-=(1,5,4) and Q-=(4,1,-2) find the direction ratios of vec(PQ)

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  7. The equations of a line are (4-x)/(2) =(y+3)/(2)=(z+2)/(1).Find the...

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  8. The Cartesian equations of a line are (x-1)/(2)=(y+2)/(3)=(5-z)/(1)...

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

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  10. Write the cartesian equation of the following line given in vector ...

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  11. Find the cartesian equation of the line which passes through the poin...

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  12. Find the Cartesian equation of a line which passes through the...

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  13. Find the angle between the lines vec r=2 hat i-5 hat j+ hat k+lambda(...

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  14. Find the angle between the pair of lines (x+3)/3=(y-1)/5=(z+3)/4and (x...

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  15. Show that the lines (x-5)/(7) =(y+2)/(-5)=(z)/(1) " and " (x)/(1) ...

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  16. The direction ratios of a line are 2,6,-9 .What are its direction...

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  17. If a line makes angles 90o," "135o," "45o with the x, y and z-axes ...

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  18. What are the direction cosines of the y-axis ?

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  19. What are the direction cosines of the vector (2hat(i)+ hat(j) -2ha...

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  20. What is the angle between the vector vec( r)=(4hat(i) +8hat(j) +...

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