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Find the vector equation of a line pa...

Find the vector equation of a line passing through `3 hat i-5 hat j+7 hat k` and perpendicular to theplane `3x-4y+5z=8.`

A

`barr=3hati-5hatj+7hatk+lambda(3hati-4hatj+5hatk)`

B

`barr=3hati-4hatj+5hatk+lambda(3hati-5hatj+7hatk)`

C

`barr=3hati+5hatj-7hatk+lambda(3hati-4hatj-5hatk)`

D

`barr=3hati+4hatj-5hatk+mu(3hati+5hatj+7hatk)`

Text Solution

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The correct Answer is:
A
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(i) Find the vector equation of a line passing through a point with position vector 2 hat(i) - hat(j) + hat(k) and parallel to the line joining the points with position vectors - hat(i) + 4 hat(j) + hat(k) and hat(i) + 2 hat(j) + 2 hat(k). Also, find the cartesian equivalent of the equation. (ii) Find the vector equation of a line passing through the point with position vector hat(i) - 2 hat(j) - 3 hat(k) and parallel to the line joining the points with position vectors hat(i) - hat(j) + 4 hat(k) and 2 hat(i) + hat(j) + 2 hat(k) . Also, find the cartesian form of the equation.

(A ) Find the vector and 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) . (b) Find the equation of a line passing through the point P(2, -1, 3) and perpendicular to the lines : vec(r) = (hat(i) + hat(j) - hat(k) ) + lambda (2 hat(i) - 2 hat(j) + hat(k)) and vec(r) = (2 hat(i) - hat(j) - 3 hat(k) ) + mu (hat(i) + 2 hat(j) + 2 hat(k)) .

Find the vector equation of a plane passing through the point having position vector 2 hat(i) + hat(j) + hat(k) and perpendicular to the vector : 4 hat(i) - 2 hat(j) + 3hat(k) .

TARGET PUBLICATION-PLANE-CRITICAL THINKING
  1. The equation of the plane passing through A(x1,y1,z1) and containg the...

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  2. Find the equation of a line passing through the point (2hati-3hatj-5h...

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  3. Find the vector equation of a line passing through 3 hat i-5 hat j+...

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  4. The equation of a line passing through point (1,2,3) and perpendicular...

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  5. The equation of the line passing through (1, 2, 3) and parallel to the...

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  6. If the angle between the planes barr.(xhati+hatj-hatk)=4" and "barr.(h...

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  7. For any four points O(0,0,0),P(1,2,1),Q(2,3,0),R(0,1,-1), the angle be...

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  8. The active angle between the plane 2x+3y-z+7=0 and X-axis is

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  9. If the angle between the line (x-1)/(1)=(y-2)/(k)=(z+3)/(4) and the pl...

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  10. Equation of a line and plane are respectively (x-1)/(2)=(y)/(3)=(z-3)/...

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  11. Equation of a line and a plane are respectively (x+3)/(2)=(y-4)/(3)=(z...

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  12. If line (x-3)/(2)=(y-4)/(3)=(z-5)/(4) lines in the plane 4x+4y-cz-d=0...

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  13. If the line (x-1)/(2)=(y-1)/(3)=(z+2)/(2) lies in the plane x+By-3z+D=...

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  14. Find the vector equation of the plane in which the lines vecr=hati+ha...

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  15. The equation of the plane containing lines (x)/(1)=(y-2)/(2)=(z+3)/(3)...

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  16. Find the equation of the plane containing the lines (x-5)/4=(y-7)/4...

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  17. The plane containing lines (x+1)/(3)=(y+3)/(5)=(z+5)/(7)" and "(x-2)/...

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  18. If lines (x+l)/(3)=(y+3)/(5)=(z+5)/(7) and (x-2)/(1)=(y-4)/(3)=(z-6)/(...

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  19. If the lines (x-2)/(1)=(y-4)/(4)=(z-6)/(k) and (x+1)/(3)=(y+3)/(5)=(z...

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  20. The lines (x-3)/(1)=(y-1)/(2)=(z-3)/(-lambda) and (x-1)/(lambda)=(y-2)...

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