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Find the vector and the Cartesian equations of the line through the point `(5, 2, 4)`and which is parallel to the vector `3 hat i+2 hat j-8 hat k`.

A

`barr=3hati+2hatj-8hatk+lambda(5hati+2hatj+4hatk),`
`(x-3)/(5)=(y-2)/(2)=(z+4)/(-4)`

B

`barr=3hati+2hatj+8hatk+lambda(5hati+2hatj-4hatk),`
`(x-3)/(5)=(y-2)/(2)=(z-8)/(-4)`

C

`barr=5hati+2hatj-4hatk+lambda(3hati-2hatj+8hatk)`
`(x-5)/(3)=(y-2)/(-2)=(z+4)/(-8)`

D

`barr=5hati+2hatj-4hatk+lambda(3hati+2hatj-8hatk)`
`(x-5)/(3)=(y-2)/(2)=(z+4)/(-8)`

Text Solution

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The correct Answer is:
D
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TARGET PUBLICATION-LINE-Critical Thinking
  1. The vector and cartesian equations of the line which passes through th...

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  2. Find the vector and the Cartesian equations of the line through the p...

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  3. Equation of a line passing through the point with position vector 2hat...

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  4. The vector equation of the line passing through (2,3,4) and parallel t...

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  5. Find the vector equation of line passing through point (1,2,-4) and pe...

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  6. The equation of line passing through the midpoint of the line joining ...

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  7. If G be centroid of the triangle with vertices (1,2,0),(0,0,2) and (2,...

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  8. The equation of line is barr=barp+t(barq-barp), where P(barp)-=(3,4,1)...

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  9. If the line joining the points P(-2,1,-8) and Q(a,b,c) is in the direc...

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  10. If x co-ordinate of a point on the line joining points (2,2,1) and (5,...

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  11. The line joining points (3,4,1) and (5,1,6) meets XY-plane at the poin...

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  12. D.c.s of a line segment AB are (-2)/(sqrt(17)),(3)/(sqrt(17)),(-2)/(sq...

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  13. The lines barr=(2hati+hatj-3hatk)+((t)/(sqrt(6)))(2hati-hatj+hatk)an...

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  14. The lines vecr=(2hati-3hatj+7hatk)+lamda(2hati+phatj+5hatk) and ve...

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  15. If the lines (x-1)/(2)=(y-1)/(lambda)=(z-3)/(0) and (x-2)/(1)=(y-3)/...

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  16. The lines and (x-1)/(3)=(y-2)/(4)=(z-3)/(5) (x-1)/(2)=(y-2)/(3)=(z-3)...

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  17. Let veca=hati+hatj and vecb=2hati-hatk. Then the point of intersection...

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  18. If the sum of the squares of the distances of a point from the three c...

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  19. The foot of perpendicular from the point (1,2,3) to the line (x)/(2)=(...

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  20. The co-ordinates of the foot of the perpendicular from the point (3,-1...

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