If `A( p,q,r )and B=(p',q',t')` are two points on the line `lambdax = muy = gammaz` such that `OA=3. OB = 4` then `pp'+qq'+rr'` is equal to

If A-=(p,q,r) and B-=(p^('),q^('),r^(')) are two points on the line lamdax=muy=vz and OA=a,OB=b where O is origin then the value of (pp^(')+qq^(')+rr^(')) is equal to

If A-=(p,q,r) and B-=(p^('),q^('),r^(')) are two points on the line lamdax=muy=vz and OA=a,OB=b where O is origin then the value of (pp^(')+qq^(')+rr^(')) is equal to (a) a+b (b) ab (c) sqrt(a^2-b^2) (d) -ab

Let A=[(1, 2),(3, 4)] and B=[(p,q),(r,s)] are two matrices such that AB = BA and r ne 0 , then the value of (3p-3s)/(5q-4r) is equal to

Let A=[(1, 2),(3, 4)] and B=[(p,q),(r,s)] are two matrices such that AB = BA and r ne 0 , then the value of (3p-3s)/(5q-4r) is equal to

In Fig. 4.238, S and T are points on the sides P Q and P R respectively of P Q R such that P T=2c m , T R=4c m and S T is parallel to Q R . Find the ratio of the areas of P S T and P Q R . (FIGURE)

If P, Q, R are 3 points on a line and Q lies between P and R, then prove that PQ=PR+RQ

In Figure, S and T are points on the sides P Q and P R respectively of /_\ P Q R such that P T=2c m , T R=4c m and S T is parallel to Q R . Find the ratio of the areas of /_\P S T and /_\P Q R .

On the xy plane where O is the origin, given points, A(1, 0), B(0, 1) and C(1, 1) . Let P, Q, and R be moving points on the line OA, OB, OC respectively such that overline(OP)=45t overline((OA)),overline(OQ)=60t overline((OB)),overline(OR)=(1-t) overline((OC)) with t>0. If the three points P,Q and R are collinear then the value of t is equal to A (1)/(106) B (7)/(187) C (1)/(100) D none of these

On the xy plane where O is the origin, given points, A(1, 0), B(0, 1) and C(1, 1) . Let P, Q, and R be moving points on the line OA, OB, OC respectively such that overline(OP)=45t overline((OA)),overline(OQ)=60t overline((OB)),overline(OR)=(1-t) overline((OC)) with t>0. If the three points P,Q and R are collinear then the value of t is equal to A (1)/(106) B (7)/(187) C (1)/(100) D none of these