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Show that each of the given three vector...

Show that each of the given three vectors is a unit vector: `1/7 (2 hat i + 3 hat j + 6 hat k)`, `1/7(3 hat i - 6 hat j + 2 hat k)`, `1/7 (6 hat i + 2 hat j - 3 hat k)` Also, show they are mutually perpendicular to each other.

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The correct Answer is:
`vec a. vec b = 0, vec b. vec c = 0` and `vec a.vec c = 0`
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Find the projection of the vector hat i + 3 hat j + 7 hat k on the vector 7 hat i - hat j + 8 hat k .

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NEW JOYTHI PUBLICATION-VECTOR ALGEBRA-SOLUTIONS TO NCERT TEXT BOOK EXERCISE 10.3
  1. Find the angle between two vectors vec a and vec b with magnitudes sqr...

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  2. Find the angle between the vectors hat i - 2 hat j + 3 hat k and 3 hat...

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  3. Find the projection of the vector hat i + hat j on the vector hat i - ...

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  4. Find the projection of the vector hat i + 3 hat j + 7 hat k on the vec...

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  5. Show that each of the given three vectors is a unit vector: 1/7 (2 hat...

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  6. Find |veca| and |vec b|, if (vec a + vec b).(vec a - vec b ) = 7 and |...

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  7. Evaluate the product (3 vec a + 5 vec b).(2 vec a + 7 vec b).

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  8. Find the magnitude of two vectors vec a and vec b having the same magn...

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  9. Find |vec x|, if for a unit vector vec a, (vec x - vec a)(vec x + vec ...

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  10. If vec a = 2 hat i + 2 hat j + 3 hat k, vec b = - hat i + 2 hat j + ha...

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  11. Show that |vec a| vec b + |vec b| vec a, is perpendicular to |vec a| v...

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  12. If vec a. vec a = 0 and vec a. vec b = 0 the what can be concluded abo...

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  13. If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c ...

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  14. If either vector vec a = vec 0 or vec b = vec 0, then veca.vec b = 0.B...

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  15. If the vertices A,B, C of a triangle ABC are (1,2,3),(-1, 0,0), (0, 1,...

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  16. Show that the points A(1,2,7), B(2,6,3) and C(3, 10, -1) are collinear...

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  17. Show that the vectors 2 hat i - hat j + hat k, hat i - 3 hat j - 5hat ...

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  18. If veca is a non zero vector of magnitude 'a' and lambda a nonzero sca...

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