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If bar(c) = 3 bar(a) - 2 bar(b) then pr...

If `bar(c) = 3 bar(a) - 2 bar(b)` then prove that `[(bar(a),bar(b),bar(c))] = 0`

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Let bar(a) be a unit vector bar(b)=2bar(i)+bar(j)-bar(k) and bar(c)=bar(i)+3bar(k) then maximum value of [[bar(a),bar(b),bar(c)]] is

Using properties of scalar triple product, prove that [(bar(a) + bar(b),bar(b) + bar(c), bar(c) + bar(a))] = 2 [(bar(a),bar(b),bar(c))]

If bar(a),bar(b),bar(c) are coplanar then the value of |[bar(a),bar(b),bar(c)],[bar(a)*bar(a),bar(a)*bar(b),bar(a)*bar(c)],[bar(b).bar(a),bar(b)*bar(b),bar(b)*bar(c)]|=

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If bar(a),bar(b)andbar(c) are any three vectors, prove that (1) [bar(a)+bar(b) bar(b)+bar(c) bar(c)+bar(a)]=2[bar(a)bar(b)bar(c)] (2) [bar(a) bar(b)+bar(c) bar(a)+bar(b)+bar(c)]=0

If bar(a),bar(b),bar(c) are any three vectors, prove that (1) [bar(a)+bar(b)" "bar(a)+bar(c)" "bar(b)]=[bar(a)" "bar(c)" "bar(b)] (2) [bar(a)-bar(b)" "bar(b)-bar(c)" "bar(c)-bar(a)]=0 .

bar(a) , bar(b) and bar(c) are three vectors such that bar(a) + bar(b) + bar(c) = bar(0) and |bar(a)| =2, |bar(b)| =3, |bar(c)| =5 ,then bar(a) . bar(b) + bar(b) . bar(c) + bar(c) . bar(a) equals

NAVNEET PUBLICATION - MAHARASHTRA BOARD-QUESTION BANK 2021-VECTOR AND THREE DIMENSIONAL GEOMETRY
  1. Show that following points are collinear P(4, 5, 2), Q(3, 2, 4), R(5, ...

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  2. If a vector has direction angles 45^(@) and 60^(@) find the third dire...

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  3. If bar(c) = 3 bar(a) - 2 bar(b) then prove that [(bar(a),bar(b),bar(c...

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  4. If |bar(a).bar(b)| = |bar(a) xx bar(b)| & bar(a). bar(b) lt 0, then fi...

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  5. The direction ratios of a vector perpendicular to the two lines whose ...

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  6. If bar(a), bar(b) and bar(c) are position vectors of the points A, B, ...

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  7. If bar(a) and bar(b) are two vectors perpendicular each other, prove t...

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  8. Find the position vector of point R which divides the line joining the...

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  9. Find a unit vector perpendicular to the vectors hat(j) + 2 hat(k) & ha...

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  10. If two of the vertices of the triangle are A(3, 1, 4) and B(-4, 5, -3)...

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  11. Find the centroid of tetrahedron with vertices K(5, -7, 0), L(1, 5, 3)...

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  12. If a line has the direction ratios 4, -12, 18, then its direction cos...

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  13. Show that the points A(2, -1, 0) B(-3, 0, 4), C(-1, -1, 4) and D(0, -5...

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  14. Using properties of scalar triple product, prove that [(bar(a) + bar(b...

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  15. The direction ratios of AB are -2,2,1. If A -= (4,1,5) and l(AB) = 6 u...

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  16. If G(a,2,-1) is the centroid of the triangle with vertices P(1,3,2),Q(...

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  17. If G(r, (-4)/(3), (1)/(3)) is centroid of the triangle having vertices...

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  18. Prove that an angle inscribed in a semi-circle is a right angle usi...

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  19. Prove using vectors: Medians of a triangle are concurrent.

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  20. Show that the perpendicular bisectors of the sides of a triangle are c...

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