Class 12

Math

3D Geometry

Three Dimensional Geometry

The direction ratios of two lines are $a,b,c$ and $(b−c),(c−a),(a−b)$ respectively. The angle between these lines is

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The lines which intersect the skew lines $y=mx,z=c;y=−mx,z=−c$ and the x-axis lie on the surface: (a.) $cz=mxy$ (b.) $xy=cmz$ (c.) $cy=mxz$ (d.) none of these

Under what condition are the two linesy=mℓx+α,z=nℓx+β; and y=m′ℓ′x+α′,z=n′ℓ′x+β′ Orthogonal?

Find the equation of a line which passes through the point $(1,1,1)$ and intersects the lines $2x−1 =3y−2 =4z−3 and1x+2 =2y−3 =4z+1 ˙$

What is the distance between the planesx−2y+z−1=0 and−3x+6y−3z+2=0?

If $A(3,2,−4),B(5,4,−6)andC(9,8,−10)$ are three collinear points, then find the ratio in which point $C$ divides $AB˙$

If $r$ is a vector of magnitude 21 and has direction ratios $2,−3and6,$ then find $r˙$

Find the locus of appoint which moves such that the sum of the squares of its distance from the points $A(1,2,3),B(2,−3,5)andC(0,7,4)is120.$

The centre of the circle given by $ri^+2j^ +2k^˙ =15and∣∣ r−(j^ +2k^)∣∣ =4$ is a. $(0,1,2)$ b. $(1,3,5)$ c. $(−1,3,4)$ d. none of these