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A line passes through the point with ...

A line passes through the point with position vector `2 hat i-3 hat j+4 hat k` and is in the direction of `3 hat i+4 hat j-5 hat kdot` Find the equations of the line in vector and Cartesian forms.

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Since the line passes through `2hati-3hatj+4hatk` and has direction of `3hati+4hatj-5hatk`, its vector equation is
`" "vecr=hata+lamdahatbrArrvecr=2hati-3hatj+4hatk+lamda(3hati+4hatj-5hatk)`, where `lamda` is a parameter.`" "`(i)
Cartesian equivalent of (i) is `(x-2)/(3)=(y+3)/(4)=(z-4)/(-5)`
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CENGAGE PUBLICATION-THREE DIMENSIONAL GEOMETRY-All Questions
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  2. The Cartesian equations of a line are 6x-2=3y+1=2z-2. Find its dire...

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  3. A line passes through the point with position vector 2 hat i-3 hat ...

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  4. Find the plane of the intersection of x^2+y^2+z^2+2x+2y+2=0 and 4x^2...

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  5. Let l1a n dl2 be the two skew lines. If P ,Q are two distinct points o...

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  6. If the lines (x-1)/(-3)=(y-2)/(2k)=(z-3)/(-2) and (x-1)/(3k)=(y-5)/1=(...

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  7. Find the angle between the lines 2x=3y=-z and 6x=-y=-4z

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  8. Find the length of the perpendicular drawn from the point(5,4,-1) t...

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  9. The equations of motion of a rocket are x=2t ,y=-4ta n dz=4t , wher...

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  10. Find the shortest distance between the lines vec r=(1-lambda) hat i...

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  11. Find the image of the point (1, 2, 3) in the line (x-6)/(3)=(y-7)/(2)=...

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  12. If the lines (x-1)/2=(y+1)/3=(z-1)/4a n d(x-3)/1=(y-k)/2=z/1 intersect...

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  13. Find the shortest distance between the z-axis and the line, x+y+2z-3=0...

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  14. The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c a...

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  15. Distance of the point P( vec p) from the line vec r= vec a+lambda ve...

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  16. The direction ratios of a normal to the plane through (1,0,0)a n d(...

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  17. The centre of the circle given by vec r.( hat i+2 hat j+2 hat k)=15...

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  18. Two systems of rectangular axes have the same origin. If a plane cu...

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  19. The plane, which passes throught the point (3,2,0) and line (x - 3)/1 ...

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  20. The lines (x-2)/1=(y-3)/1=(z-4)/-k and (x-1)/k=(y-4)/2=(z-5)/1 are co...

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