Write the cartesian equation of the stra...

Write the cartesian equation of the straight line through the point (1,2,3) and along the vector `3hati+hatj+2hatk`

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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 3hati+2hatj-8hatk

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 3hati + 2hatj - 2hatk

Find the vectoer and cartesian equations of the line through the point (1,2,-4) and perpendicualr of the lines: vecr=(8hati-19hatj+10hatk)+lambda(3hati-16hatj+7hatk) and vecr=(15hati+29hatj+5hatk)+mu(3hati+8hatj-5hatk)

Find the equation of the plane passing through the point (1,1,1) and containing the line: vecr=(-3hati+hatj+5hatk)+lambda (3hati-hatj+5hatk) . Also, show that the plane contains the line: vecr=(-hati+2hatj+5hatk)+lambda(hati-2hatj-5hatk) .

Find the vector and cartesian equations of the plane that passes through the point (1,4, 6) and the normal vector to the plane is hati-2hatj+hatk

Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, -4) and parallel to the lines vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=hati-3hatj+5hatk+mu(hati+hatj-hatk) .

Find the vector and cartesian equations of the plane that passes through the point (1, 0, – 2) and the normal to the plane is hati+hatj-hatk

Find the vector equation of the line passing through the point (3,1,2) and perpendicular to the plane vecr*2hati-hatj+hatk)=4 . Also find the point of intersection of this line and the plane.

Find the equation of the line passing through the point (1,2,-3) and perpendicular to the lines : vecr=(2hati-hatj-hatk)+lambda(2hati-hatj-3hatk) and vecr=(3hati-hatj-2hatk)+mu(hati+hatj+hatk)

Find the equation of the line passing through the point (1,-2,3) and perpendicular to the lines : vecr=(hati-2hatj+hatk)+lambda(hati+hatj+hatk) and vecr=(hati-hatj+2hatk)+mu(3hati-2hatj-5hatk)

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE

Write the cartesian equation of the straight line through the point (1...
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Find the distance of the point (2,3,4) from the x axis.
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If a line makes angles of 90^@,60^@ and theta with the x, y and z axis...
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If a line has direction cosines <2/3, -1/3, -2/3>, then find the direc...
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If a line has direction ratios <2,-1,-2>, then what are its direction ...
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Find the direction cosines of a line passing through the points (1,0,0...
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Find the direction cosines of the lines joining the points: (-1,-1,-1)...
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Find the direction ratios and direction cosines of the vector joining ...
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Write the direction cosines of the vector : -2hati+hatj-5hatk
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Write the direction cosines of the vector : hati+2hatj+3hatk
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Find the length of the projection of the line segment joining (3,4,5) ...
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Show that the following points are collinear : (1,2,3) , (2,6,3) , (3,...
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Find the acute angle between two lines whose direction ratios are <2,3...
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Find the obtuse angle between two lines whose direction ratios are : <...
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Find the angle between the lines whose direction ratios are : a,b,c...
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Find the direction cosines of the sides of the triangle whose vertices...
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Show that the three lines with direction cosines 12/13, -3/13, -4/13, ...
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The angle between the lines whose direction cosines are given by the ...
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Find the angle between the lines whose direction cosines are given by ...
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Find the area of the triangle ABC whose vertices are : A(1,2,4), B(-2,...
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Show that the line through the points (4, 7, 8), (2, 3, 4) is parallel...
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