Show that the line , vecr=hati+hatj+lamb...

Show that the line , `vecr=hati+hatj+lambda(2hati+hatj+4hatk)` lies in the plane `vecr*(hati+2hatj-hatk)=3`.

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Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) lies in the plane vecr*(3hati+hatj-hatk)+2=0 .

State when the line vecr=veca+lambdavecb is parallel to the plane vecr*vecn=d . Show that the line vecr=hati+hatj+lambda (2hati+hatk+4hatk) is parallel to the plane vecr*(-2hati+hatk)=5 . Also, find the distance between the line and the plane.

Find the angle between the line vecr=(hati+hatj+hatk)+lambda(2hati-hatj-hatk) and the plane vecr.(hati+hatj-2hatk) =3.

Find the angle between the line : vecr=(hati-hatj+hatk)+lambda(2hati-hatj+3hatk) and the plane vecr*(2hati+hatj-hatk)=4 . Also find whether the line is parallel to the plane or not.

Find the angle between the line vecr=(hati-hatj+3hatk)+lambda(2hati-hatj+hatk) and the plane vecr.(hati+hatj+2hatk) =4.

True or false The line vecr=2hati-3hatj+hatk+t(hati-hatj+2hatk) lies in the plane vecr.(3hati+hatj-hatk)-2=0 .

Find the distance of the point (2,12,5) from the point of intersection of the line: vecr=2hati-4hatj+2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr*(hati-2hatj+hatk)=0 .

Find the angle between the line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and the plane vecr.(2hati-hatj+hatk)=4 .

Find the angles between the line vecr=-hati+hatj+2hatk+lambda(3hati+2hatj+4hatk) and the plane vecr.(2hati+hatj-3hatk)+4=0

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE

Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in t...
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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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