Let r-1-r-2-r-3-r-n- be the position vectors of points P1-P2-P3-Pn relative to the origin O- If the vector equation a1r-1-a2r-2-anr-n-0 holds- then a similar equation will also hold w-r-t- to any other origin provided-

The correct option is C a_1+a_2+......+a_n=0 Let the new origin be at c #160; from previous origin. #160;So new position vectors are: R _ 1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Equation of a Plane Passing through a Point and Perpendicular to a Given Vector

Let r̅̅1̅,r...

Question

Let $_{1},_{2},_{3} . . . . . . . . . ._{n},$ be the position vectors of points $P_{1^{'}} P_{2^{'}} P_{3^{'}} . . . . . . . . P_{n}$ relative to the origin O. If the vector equation $a_{1}_{1} + a_{2}_{2} + . . . . . . . . . + a_{n}_{n} = 0$ holds, then a similar equation will also hold w.r.t. to any other origin provided:

a_{1} + a_{2} + . . . . . . + a_{n} = n

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a_{1} + a_{2} + . . . . . . + a_{n} = 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a_{1} + a_{2} + . . . . . . + a_{n} = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

none

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

Suggest Corrections

Similar questions

_{1},_{2},_{3}, . . . . . . ._{n}

P_{1}, P_{2}, P_{3}, . . . . . ., P_{n}

O

a_{1}_{1} + a_{2}_{2} + . . . . . . + a_{n}_{n} = 0

a_{1} > a_{2} > a_{3} > . . . . > a_{n} > 1.

p_{1} > p_{2} > p_{3} > . . . . > p_{n} > 0

p_{1} + p_{2} + p_{3} + . . . + p_{n} = 1.

F (x) = (p_{1} a_{1}^{x} + p_{2} a_{2}^{x} + . . . + p_{n} a_{n}^{x})^{1 / x}

{lim}_{x \to 0^{+}} F (x)

a_{1} > a_{2} > a_{3} > . . . . > a_{n} > 1.

p_{1} > p_{2} > p_{3} > . . . . > p_{n} > 0

p_{1} + p_{2} + p_{3} + . . . + p_{n} = 1.

F (x) = (p_{1} a_{1}^{x} + p_{2} a_{2}^{x} + . . . + p_{n} a_{n}^{x})^{1 / x}

lim x \to - \infty F (x)

a_{1} > a_{2} > a_{3} > . . . . > a_{n} > 1.

p_{1} > p_{2} > p_{3} > . . . . > p_{n} > 0

p_{1} + p_{2} + p_{3} + . . . + p_{n} = 1.

F (x) = (p_{1} a_{1}^{x} + p_{2} a_{2}^{x} + . . . + p_{n} a_{n}^{x})^{1 / x}

{lim}_{x \to \infty} F (x)

a_{1} > a_{2} > a_{3} > \dots a_{n} > 1;

p_{1} > p_{2} > p_{3} > . . . p_{n} > 0

p_{1} + p_{2} + p_{3} + \dots + p_{n} = 1.

F (x) = {(p_{1} a_{1}^{x} + p_{2} a_{2}^{x} + \dots + p_{n} a_{n}^{x})}_{1}^{1 / x},

Join BYJU'S Learning Program