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Syllabus

^{- }+ QR^{- }=2MN-here

^{-}means barQ. If u,v,w are non-coplanar vectors and p, q are real numbers, then the equality

$\left[\overline{u}\overline{v}\overline{w}\right]-pq\left[\overline{u}\overline{v}\overline{w}\right]+2{q}^{2}\left[\overline{u}\overline{v}\overline{w}\right]=0$ holds for

a. exactly one value of (p, q)

b. exactly two values of (p, q)

c. more than two but not all values of (p,q)

d. all values of (p,q)

Plz answer it urgently..

(a) l+m+n (b) l^3+m^3+n^3

(c) l^2+m^2+n^2

(d) None of these

How to do cross product in vectors?

(1) $\frac{3\mathrm{\pi}}{4}$

(2) $\frac{\mathrm{\pi}}{2}$

(3) $\frac{2\mathrm{\pi}}{3}$

(4) $\frac{5\mathrm{\pi}}{6}$

area is 2, then the value of b is

(a) -1 (b) 3 (c) -3

(d) 1

- the ratio in which the point C divides the line segment AB
- the values of p and q

9. If the points A(3 , 0) , B(-1 , 3) and C(-3 , 3, 0) are collinear, then find

(i) the ratio in which the point C divides the line segment AB.

(ii) the values of p and q.

$41.\mathrm{If}\mathrm{G}\left(\overline{\mathrm{g}}\right).\mathrm{H}\left(\overline{\mathrm{h}}\right)\mathrm{and}\mathrm{P}\left(\overline{\mathrm{p}}\right)\mathrm{are}\mathrm{centrold},\mathrm{orthocenter}\mathrm{and}\mathrm{circumcenter}\mathrm{of}\mathrm{a}\mathrm{triangle}\mathrm{and}\phantom{\rule{0ex}{0ex}}\mathrm{x}\overline{\mathrm{p}}+\mathrm{y}\overline{\mathrm{h}}+\mathrm{z}\overline{\mathrm{g}}=0\mathrm{then}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\mathrm{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}\phantom{\rule{0ex}{0ex}}\left(\mathrm{A}\right)1,1,-2\left(\mathrm{B}\right)2,1,-3\left(\mathrm{C}\right)1,3,-4\left(\mathrm{D}\right)2,3,-5\phantom{\rule{0ex}{0ex}}$

Plz find out