Show that [veca+vecbvecb+veccvecc+veca] ...

Show that `[veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]`

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THREE DIMENSIONAL GEOMETRY
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Prove that [vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2

Show that veca, vecb and vec c are coplanar if veca+vecb,vecb+vecc and vecc+veca are coplanar.

For any three vectors veca,vecb,vecc show that [(veca-vecb) (vecc-veca) (vecb-vecc)] = 0

Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb) . Interpret this result geometrically.

For veca = hati+hatj, vecb = -hati+2hatk, vecc = hatj+hatk , obtain vecaxx(vecbxxvecc) and also verify the formula vecaxx(vecbxxvecc) = (veca.vecc)vecb-(veca.vecb)vecc .

If veca, vecb, vecc are mutually perpendicular vectors of equal magnitude, show that veca+vecb+vecc is equally inclined to veca.vecb.vecc .

If a and b are perpendicular vectors show that (veca+vecb)^2 = (veca-vecb)^2 . [(veca+vecb)^2 means (veca+vecb).(veca+vecb) , so does (veca-vecb)^2 .]

If veca,vecb,vecc are such that veca.vecb = veca.vecc then show that veca = vec0 or vecb = vecc or veca is perpendicular to vecb.vecc .

|veca| = |vecb| = veca = vecb .

Prove that the four points with position vectors 2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc and veca-6vecb+6vecc are coplanar.

SHARAM PUBLICATION-VECTORS-EXAMPLE

Prove that [vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2
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Let vec(a) = hat(i) + hat(j) + hat(k), vec(b) = 4hat(i) - 2hat(j) + 3h...
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Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]
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If veca+vecb+vecc = vec0, |veca| = 3 , |vecb| = 5 and |vecc| = 7, find...
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The position vectors of the points A, B, C and D are 4hati+3hatj-hatk,...
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If the sum of two unit vectors is a unit vectors find the magnitude of...
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If veca = (2,-2,1), vecb = (2,3,6) and vecc = (-1,0,2), Find the magni...
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Prove the following by vector method. An angle inscribed in a semi-cir...
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If veca, vecb and vecc mutually perpendiculars, show that [veca.(vecbx...
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If hati +hatj+hatk and 2hati -alphahatj+3hatk are orthogonal to each o...
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Find [veca vecb vecc] when veca= hati -2hatj + 3hatk, vecb=2hati+ hatj...
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Find a vectorvecb such that vecaxxvecb=vecc and veca.vecb = 3 where ve...
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Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...
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Determine the area of the parallelogram whose sides are the vectors 2h...
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If the position vectors of the points A, B, C are 2hat(i) + hat(j) - h...
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Find the scalar projection of the vector veca = 3hati+6hatj + 9hatk on...
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Find the value of lambda such that the following vectors are coplanar:...
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Prove that four points with position vectors hati+hatj-3hatk, 2hati -h...
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Using vector method find the area of the triangle with vertices (1, 0,...
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Write the volume of the parallelopiped whose sides are given by-hatj, ...
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