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If A=(3,1,-2) ; B=(-1,0,1) and l,m are p...

If A=(3,1,-2) ; B=(-1,0,1) and l,m are projections of AB on y-axis, zx plane respectively, then `3l^2-m+1=`
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Conside the matrices A=[(1,2,3),(4,1,2),(1,-1,1)] B=[(2,1,3),(4,1,-1), (2,2,3)] C=[(14),(12),(2)] D=[(13),(11),(14)] . Now x=[(x),(y),(z)] is such that solutions of equation AX=C and BX=D represent two points L andM respectively in 3 dimensional space. If L' and M' are hre reflections of L and M in the plane x+y+z=9 then find coordinates of L,M,L',M'

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If l_(1), m_(1), n_(1), l_(2), m_(2), n_(2) and l_(3), m_(3), n_(3) are direction cosines of three mutuallyy perpendicular lines then, the value of |(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3))| is

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The moment of inertia of a thin square plate ABCD, fig, of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is where l_1, l_2, l_3 and l_4 are respectively the moments of intertial about axis 1,2,3 and 4 which are in the plane of the plate.

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Statement-I (S_1) : If A(x_1, y_1), B(x_2, y_2), C(x_3, y_3) are non-collinear points. Then, every point (x, y) in the plane of triangleABC , can be expressed in the form ((kx_1+lx_2+mx_3)/(k+l+m), (ky_1+ly_2+my_3)/(k+l+m)) Statement-II (S_2) The condition for coplanarity of four A(a), B(b), C(c), D(d) is that there exists scalars l, m, n, p not all zeros such that la+mb+nc+pd=0 where l+m+n+p=0 .

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