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The position vectors of the points A, B,...

The position vectors of the points A, B, C are `2 hati + hatj - hatk , 3 hati - 2 hatj + hatk and hati + 4hatj - 3 hatk ` respectively . These points

A

form an isosceles triangle

B

form a right triangle

C

are collinear

D

form a scalene triangle

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If the position vectors of the three points A,B,C are 2hati+4hatj-hatk, hati+2hatj-3hatk and 3hati+hatj+2hatk respectively, find a vector perpendicular to the plane ABC.

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Find a unit vector perpendicular to plane ABC when position vectors of A,B,C are 3 hati - hatj + 2hatk, hati - hatj- 3hatk and 4 hati - 3 hatj + hatk respectively.

The position vectors of vertices of a DeltaABC are 4hati - 2 hatj , hati + 4hatj - 3hatk and -hati + 5hatj + hatk respectively , then angleABC is equal to

The position vectors of points A,B and C are hati+hatj,hati + 5hatj -hatk and 2hati + 3hatj + 5hatk , respectively the greatest angle of triangle ABC is

If the position vector of the vertices A,B and C of a DeltaABC be (hati + 2hatj + 3hatk), (2hati + 3hatj + hatk) and (3hati + hatj +2hatk) respectively, prove that DeltaABC is equilateral.

OBJECTIVE RD SHARMA-ALGEBRA OF VECTORS-Chapter Test
  1. In a quadrilateral ABCD, vec(AB) + vec(DC) =

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  2. If ABCDE is a pentagon, then vec(AB) + vec(AE) + vec(BC) + vec(DC) +...

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  3. If ABCD is a parallelogram, then vec(AC) - vec(BD) =

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  4. In a Delta ABC, " if " vec(AB) = hati - 7hatj + hatk and vec(BC) = 3 ...

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  5. In a Delta ABC, if vec(AB) = 3 hati + 4 hatk, vec(AC) = 5 hati + 2 hat...

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  6. The position vectors of P and Q are respectively vec a and vec b . If ...

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  7. If the points whose position vectors are 2hati + hatj + hatk , 6hati -...

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  8. The ratio in which hati + 2 hatj + 3 hatk divides the join of -2hati ...

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  9. If OACB is a parallelogramwith vec(OC) = vec a and vec (AB) = vec b...

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  10. The position vectors of the points A, B, C are 2 hati + hatj - hatk , ...

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  11. If ABCDEF is a regular hexagon then vec(AD)+vec(EB)+vec(FC) equals :

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  12. If the points with position vectors 20 hati + p hatj , 5 hati - hat...

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  13. If the position vector of a point A is vec a + 2 vec b and vec a divi...

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  14. If vec a ,\ vec b ,\ vec c and vec d are the position vectors of p...

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  15. Let G be the centroid of Delta ABC , If vec(AB) = vec a , vec(AC) = v...

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  16. If G is the intersection of diagonals of a parallelogram ABCD and O is...

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  17. The vector cos alpha cos beta hati + cos alpha sin beta hatj + sin a...

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  18. In a regular hexagon ABCDEF, vecAB=a, vecBC=b and vecCD = c. Then, vec...

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  19. If three points A, B and C have position vectors hati + x hatj + 3 ha...

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  20. If the position vectors of the vertices of a triangle of a triangle ar...

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