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Show that the point A , B and C with pos...

Show that the point `A , B` and `C` with position vectors ` vec a` =3` hat i` - 4` hat j` -4` hat k` ` vec b`= 2` hat i` `j` + ` hat k` and ` vec c` = ` hat i` - 3` hat j` - 5` hat k`, respectively form the vertices of a right angled triangle.

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Show that the points A, B and C with position vectors, veca=3 hat i-4 hat j-4 hat k , vecb=2 hat i- hat j+ hat k and vecc= hat i-3 hat j-5 hat k respectively form the vertices of a right angled triangle.

Show that the points A ,\ B\ a n d\ C with position vectos vec a=3 hat i-4 hat j-4 hat k ,\ vec b=2 hat i- hat j+ hat k\ a n d\ vec c= hat i-3 hat j-5 hat k represent, form the vertices of a right angled triangle.

Show that the points A, B, C with position 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 respectively, are the vertices of a right angled triangle. Also, find the remaining angles of the triangle.

Find the sum of vectors vec a= hat i-2 hat j+ hat k ,\ vec b=-2 hat i+4 hat j+5 hat k\ a n d\ vec c= hat i-6 hat j-7 hat kdot

Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 hat i+4 hat j-2 hat k\ a n d\ vec c=4 hat i-2 hat j-2 hat k are coplanar.

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 points whose position vectors are vec a=4 hat i-3 hat j+k ,\ vec b=2 hat i-4 hat j+5k ,\ vec c= hat i- hat j form a right triangle.

If vec a=3 hat i- hat j-4 hat k , vec b=2 hat i+4 hat j-3 hat k and vec c= hat i+2 hat j- hat k , find |3 vec a-2 hat b+4 hat c|dot

Find the projection of vec b+ vec c on vec a where vec a=2 hat i-\ 2 hat j+\ hat k ,\ vec b=\ hat i+\ 2 hat j-\ 2 hat k and vec c=2 hat i-\ hat j+\ 4 hat k

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. The vector hat i+x hat j+3 hat k is rotated through an angle theta an...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. If A(-4,0,3) and B(14 ,2,-5), then which one of the following points l...

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