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Find the vector equation of a sphere wit...

Find the vector equation of a sphere with centre having the position vector `hat(i)+hat(j)+hat(k) and sqrt(3).`

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The correct Answer is:
`|r-(hat(i)+hat(j)+hat(k))|=sqrt(3)`
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Find the vector equation of a line passing through the point having the position vector (hat(i)+2hat(j) -3hat(k)) and parallel to the line joining the points with position vectors (hat(i) -hat(j) +5hat(k)) and (2hat(i) +3hat(j) -4hat(k)) .Also find the Cartesian equivalents of this equations.

Find the equation of the sphere whose centre has the position vector 3hat(i)+6hat(j)-4hat(k) and which touches the plane r*(2hat(i)-2hat(j)-hat(k))=10 .

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) .

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

Find the vector equations of the line passing through the point with position vector (2hat(i) +hat(j) -5hat(k)) and parallel to the vector (hat(i) +3hat(j) -hat(k)) .Deduce the Cartesian equations of the line .

Find the vector equation of a line passing through a point with position vector 2hat i-hat j+hat k ,and parallel to the line joining the points -hat i+4hat j+hat k and hat i+2hat j+2hat k. Also, find the cartesian equivalent of this equation.

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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Find the vector equation of a sphere with centre having the position v...

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  2. Consider a pyramid OPQRS located in the first octant (xge0, yge0, zge0...

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  3. Let P be the image of the point (3, 1, 7) with respect to the plane x...

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  4. From a point P(lambda, lambda, lambda), perpendicular PQ and PR are dr...

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  5. Two lines L(1) : x=5, (y)/(3-alpha)=(z)/(-2) and L(2) : x=alpha, (y)/(...

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  6. A line l passing through the origin is perpendicular to the lines 1:...

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  7. Perpendicular are drawn from points on the line (x+2)/(2)=(y+1)/(-1)=...

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  8. If the straight lines (x-1)/(2)=(y+1)/(k)=(z)/(2) and (z+1)/(5)=(y+1)/...

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  9. If the distance between the plane Ax-2y+z=d and the plane containing ...

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  10. Read the following passage and answer the questions. Consider the line...

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  11. Read the following passage and answer the questions. Consider the line...

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  12. Read the following passage and answer the questions. Consider the line...

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  13. Consider three planes P(1):x-y+z=1 P(2):x+y-z=-1 and " "P...

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  14. Consider the planes 3x-6y-2z=15a n d2x+y-2z=5. Statement 1:The parame...

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  15. If the image of the point P(1,-2,3) in the plane, 2x+3y-4z+22=0 measur...

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  16. The distance of the point (1, 3, -7) from the plane passing through th...

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  17. The distance of the point (1,-5,""9) from the plane x-y+z=5 measured a...

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  18. If the line, (x-3)/2=(y+2)/(-1)=(z+4)/3 lies in the place, l x+m y-z=9...

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  19. The disatance of the point (1, 0, 2) from the point of intersection of...

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  20. The equation of the plane containing the line 2x-5y+z=3, x+y+4z=5 and ...

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  21. The angle between the lines whose direction cosines satisfy the equ...

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