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Show that the vector hat i+ hat j+ hat ...

Show that the vector ` hat i+ hat j+ hat k` is equally inclined with the coordinate axes.

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`vec(a).hat(i)=|vec(a)||hat(i)|cos alpha implies sqrt(3)xx1xx cos alpha =1 implies cos alpha = 1/sqrt(3)`.
Similarly, `cos beta = 1/sqrt(3)` and `cos gamma=1/sqrt(3)`.
`:. alpha =beta=gamma= cos^(-1) (1/sqrt(3))`
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RS AGGARWAL-SCALAR, OR DOT, PRODUCT OF VECTORS-Exercise 23
  1. if veca is a unit vector and (vecx-veca).(vecx+veca)=8 then |vecx|

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  2. Find the angles which the vector vec(a)=3 hat(i)-6hat(j)+2hat(k) makes...

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  3. Show that the vector hat i+ hat j+ hat k is equally inclined with the...

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  4. Find a vector vec a of magnitude 5sqrt(2) making an angle pi/4 with x-...

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  5. Find the angle between (vec(a)+vec(b)) and (vec(a)-vec(b)), if vec(a)=...

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  6. Express the vector vec(a)=(6hat(i)-3hat(j)-6hat(k)) as sum of two vect...

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  7. Prove that ( -> a+ -> b)dot( -> a+ -> c)| -> a|^2+| -> b|^2 , if and o...

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  8. If vec a+ vec b+ vec c=0,| vec a|=3,| vec b|=5,| vec c|=7, then find ...

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  9. Find the angle between vec(a) and vec(b), when (i) |vec(a)|=2, |vec(...

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  10. Find | -> a- -> b|, if two vector -> a and -> b are such that | -> a...

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  11. Find | vec a|a n d\ | vec b| , if : ( vec a+ vec b)dot( vec a- vec b)=...

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  12. If hat a\ a n d\ hat b are unit vectors inclined at an angle theta t...

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  13. Dot product of a vector with hat i+ hat j-3 hat k , hat i+3 hat j-2 h...

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  14. If vec(AB)=(3hat(i)-hat(j)+2hat(k)) and the coordinates of A are (0, -...

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  15. If A(2, 3, 4), B(5, 4, -1), C(3, 6, 2) and D(1, 2, 0) be four points, ...

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  16. Find the value of lambdadot If the vectors 2 hat i+lambda hat j+3 hat ...

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  17. Show that the vectors vec a=3 hat i-2 hat j+ hat k ,\ vec b= hat i-3...

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  18. Three vertices of a triangle are A(0, -1, -2), B(3, 1, 4) and C(5, 7, ...

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  19. If the position vectors of the vertices a, B and C of a Triangle ABC b...

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  20. If vec a and vec b are two non-collinear unit vectors such that |...

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