class 12

Math

3D Geometry

Three Dimensional Geometry

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$and $l_{2}=m_{2}+n_{2}$is

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A mirror and a source of light are situated at the origin 0 and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the direction ratios of the normal to the plane are 1, -1, 1, then direction consines of the reflected rays are

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

Find the value of $m$ for which thestraight line $3x−2y+z+3=0=4x+3y+4z+1$ is parallel to the plane $2x−y+mz−2=0.$

Find Cartesian and vector equation of the line which passes through the point $(−2,4,−5)$ and parallel to the line given by $3x+3 =5y−4 =6z+8 $ .

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

Find the equation of the sphere described on the joint of points $AandB$ having position vectors $2i^+6j^ −7k^and−2i^+4j^ −3k^,$ respectively, as the diameter. Find the center and the radius of the sphere.

Let A(a⃗ ) and B(b⃗ ) be points on two skew line r⃗ =a⃗ +λ⃗ and r⃗ =b⃗ +uq⃗ and the shortest distance between the skew line is 1, where p⃗ and q⃗ are unit vectors forming adjacent sides of a parallelogram enclosing an area of 12units. If an angle between AB and the line of shortest distance is 60∘, then AB=

Find the equation of the plane passing through the line $5x−1 =6y+2 =4z−3 $ and point $(4,3,7)˙$