Three Dimensional Geometry
Find the angle between the planes r⋅(i^+j^)=1 and r⋅(i^+k^)=3.
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Value of λ
such that the line 2x−1=3y−1=λz−1
to normal to the plane r2i+3j+4k˙=0
d. none of these
The ratio in which the line segment joining the points whose position vectors are 2i^−4j^−7k^and−3i^+5j^−8k^
is divided by the plane whose equation is r^i^−2j^+3k^˙=13
internally b. 12:25
internally d. 37:25
Find the vector equation of the following planes in Cartesian form:
is the origin, OP=3
with direction ratios −1,2,and−2,
then find the coordinates of P˙
are two lines, then find the equation of acute angle bisector of two lines.
Find the equations of the bisectors of the angles between the planes 2x−y+2z+3=0and3x−2y+6z+8=0
and specify the plane which bisects the acute angle and the plane which bisects the obtuse angle.
Distance of the point P(p) from the line r=a+λb is a. ∣∣(a−p)+∣∣b∣∣2((p−a)b˙)b∣∣ b. ∣∣(b−p)+∣∣b∣∣2((p−a)b˙)b∣∣ c. ∣∣(a−p)+∣∣b∣∣2((p−b)b˙)b∣∣ d. none of these
Find the ratio in which the y−z
plane divides the join of the points (−2,4,7)and(3,−5,8)˙