SKEW LINES | ANALYTICAL GEOMETRY | UPSC MATHEMATICS OPTIONAL | KARAN SONI

STATEMENT-1 : The shortest distance between the skew lines (x+3)/-4=(y-6)/3=\z/2 and (x+2)/-4=y/1=(z-7)/1 is 9. and STATEMENT-2 : Two lines are skew lines if there doesn't exist a plane passing through them.

Assertion: The shortest distance between the skew lines (x+3)/(-4)=(y-6)/3=z/2 and (x+2)/(-4)=y/1=(z-7)/1 is 9., Reason: Two lines are skew lines if there exists no plane passing through them. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: The shortest distance between the skew lines vecr=veca+alphavecb and vecr=vecc+beta vecd is (|[veca-vecc vecb vecd]|)/(|vecbxxvecd|) , Reason: Two lines are skew lines if they are not coplanar. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

STATEMENT-1 : Magnetic poles are only mathematical assumptions and have no real existence . and STATEMENT-2 : Magnetic field lines are always in closed loops .

Figure shows four points A, B, C and D in uniform electric field vec(E ) . The line AB and CD are perpendicular and BC and AD are parallel to the field lines. If V_(A), V_(B) , V_(C ) and V_(D) are electric potential at A, B,C,D choose the correct option.

The base of the pyramid A O B C is an equilateral triangle O B C with each side equal to 4sqrt(2),O is the origin of reference, A O is perpendicualar to the plane of O B C and | vec A O|=2. Then find the cosine of the angle between the skew straight lines, one passing though A and the midpoint of O Ba n d the other passing through O and the mid point of B Cdot

If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form Option1: a square Option2: a rhombus Option3: a rectangle Option4: any other parallelogram

A tin chloride Q undergoes the following reaction (not balanced) Q+Cl − →X Q+Me 3 ​ N→Y Q+CuCl 2 ​ →Z+CuCl X is monoanion having pyramidal geometry. Both Y and Z are neutral compounds. Choose the correct options(s)