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Prove that point hat i +2 hat j - 3 hat...

Prove that point ` hat i` +2` hat j` - 3` hat k` ,2` hat i` - ` hat j` + ` hat k` and 2` hat i` + 5` hat j` - ` hat k` from a triangle in space.

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Prove that the four points 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ,3 hat j-6 hat k and 2 hat i+5 hat j+10 hatk form a tetrahedron in space.

Prove that the points hat i- hat j ,4 hat i-3 hat j+ hat k and 2 hat i-4 hat j+5 hat k are the vertices of a right angled triangle.

Prove that the points hat i- hat j ,4 hat i-3 hat j+ hat k and 2 hat i-4 hat j+5 hat k are the vertices of a right angled triangle.

Show that the vectors 2 hat i- hat j+ hat k , hat i-3 hat j-5 hat k and 3 hat i-4 hat j-4 hat k form the vertices of a right angled triangle.

Prove that the following vectors are coplanar: 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k\ a n d\ 3 hat i-4 hat j-4 hat k

Prove that the following vectors are non-coplanar: hat i+2 hat j+3 hat k ,2\ hat i+ hat j+3 hat k\ a n d\ hat i+ hat j+ hat k

Prove that the following vectors are coplanar: hat i+ hat j+ hat k ,\ 2 hat i+3 hat j- hat k\ a n d- hat i-2 hat j+2 hat k

Prove that the points having position vectors hat i+2 hat j+3 hat k ,\ 3 hat i+4 hat j+7 hat k ,\ -3 hat i-2 hat j-5 hat k are collinear.

Show that the points A(2 hat i- hat j+ hat k), B( hat i-3 hat j-5 hat k), C(3 hat i-4 hat j-4 hat k) are the vertices of a right angled triangle.

Show that the points A(2 hat i- hat j+ hat k), B( hat i-3 hat j-5 hat k), C(3 hat i-4 hat j-4 hat k) are the vertices of a right angled triangle.

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c...

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  2. The vector hat i+x hat j+3 hat k is rotated through an angle theta an...

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  3. Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k ...

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  4. Show that the point A , B and C with position vectors vec a =3 hat i ...

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  5. If 2vec(AC)=3vec(CB), then prove that 2vec(OA)+3vec(OB)=5vec(OC) where...

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  6. Find the unit vector in the direction of vector vec (PQ), where P and...

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  7. For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + ...

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  8. If the projections of vector vec a on x -, y - and z -axes are 2, ...

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  9. Find a vector in the direction of the vector 5 hat i - hat j + 2 h...

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  10. If vec a , vec b , vec c , vec d are the position vector of point A ,...

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  11. Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6) and D(2,-5,10)...

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  12. Statement 1: The direction cosines of one of the angular bisectors ...

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  13. Statement 1: In DeltaA B C , vec (A B)+ vec (BC)+ vec (C A)=0 State...

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  14. Statement 1: If vec ua n d vec v are unit vectors inclined at an angl...

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  15. Statement 1: If cosalpha,cosbeta,a n dcosgamma are the direction cosi...

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  16. A vector has components p and 1 with respect to a rectangular Cartesia...

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  17. Statement 1 : If three point P, Q and R have position vectors veca, ve...

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  18. In a four-dimensional space where unit vectors along the axes are h...

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  19. Let A B C be a triangle, the position vectors of whose vertices are -1...

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  20. If non-zero vectors vec a and vec b are equally inclined to coplanar ...

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