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Show that each of the given three vector...

Show that each of the given three vectors are mutually perpendicular unit vector : `(1)/(7)(2hati+3hatj+6hatk),(1)/(7)(3hati-6hatj+2hatk),(1)/(7)(6hati+2hatj-3hatk)`.

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The correct Answer is:
`vecc_|_veca`
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Show that each of the given three vectors is a unit vector : 1/7(2hati+3hatj+6hatk),1/7(3hati-6hatj+2hatk),1/7(6hati+2hatj-3hatk) . Also, show that they are mutually perpendicular to each other.

Show that the given vector is a unit vector: (1/7)(2hati + 3hatj + 6hatk)

Show that the given vector is a unit vector: (1/7)(3hati - 6hatj + 2hatk)

The unit vector perpendicular to the vectors 6hati+2hatj+3hatk and 3hati-6hatj-2hatk , is

Find a vector of magnitude 7 , which is perpendicular to both the vectors : 2hati-hatj+hatk and hati+hatj-hatk

A vectors which makes equal angles with the vectors 1/3(hati - 2hatj + 2 hatk ) , 1/5(-4hati - 3hatk) , hatj is:

The unit vector which is orthogonal to the vector 3hati + 2hatj + 6hatk and is coplanar with vectors 2hati + hatj + hatk and hati - hatj + hatk is (a) (2hati - 6hatj + hatk)/sqrt41 (b) (2hati-3hatj)/sqrt13 (c) (3 hatj -hatk)/sqrt10 (d) (4hati + 3hatj - 3hatk)/sqrt34

Show that the following vectors are coplanar : 2hati-hatj+hatk,hati-3hatj-5hatk,3hati-4hatj-4hatk .

BETTER CHOICE PUBLICATION-VECTOR ALGEBRA -SOLVED EXAMPLES SECTION III
  1. Find |vecx|, if for a unit vector veca, (vecx - veca)cdot(vecx+veca)...

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  2. Find |veca| and |vecb|, if (veca+vecb)*(veca-vecb)=8 and |veca|=8|vecb...

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  3. Find the angle between the vectors veca=hati-2hatj+3hatk and vecb=3hat...

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  4. If veca=5hati-hatj-3hatkandvecb=hati+3hatj-5hatk then show that the ve...

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  5. Find the value of lambda sach that the vectors 3veca+4vecb and 2veca+v...

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  6. Show that each of the given three vectors are mutually perpendicular u...

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  7. Prove that (veca+vecb) cdot (veca+vecb) = |veca|^2 + |vecb|^2, if and ...

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  8. Show that |veca|vecb + |vecb|veca is perpendicular to |veca|vecb-|vec...

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  9. If veca, vecb, vecc are unit vectors such that veca+vecb+vecc=0, find...

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  10. The projection of veca=2hati+3hatj+2hatk on vecb=hati+2hatj+hatk is eq...

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  11. Find lambda when the scalar projection of veca=lambdahati+hatj+4hatk o...

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  12. Show that the points : A(2hati-hatj+hatk),B(hati-3hatj-hatk),C(3hati-4...

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  13. If the vertices, A, B, C of DeltaABC have position vectors, (1,2,3),(-...

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  14. If veca=hati+4hatj+2hatk , vecb=3hati-2hatj+7hatk and vecc=2hati-hatj+...

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  15. Express the veca=5hati-2hatj+5hatk as sum of two vectors such that one...

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  16. Use vectors to prove that in triangleABC : a=bcos C+c cos B.

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  17. With the help of vector method, prove that,cosC=(a^2+b^2-c^2)/(2ab)

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  18. Find |veca X vecb|,if veca=hati-7hatj+7hatk and vecb=3hati-2hatj+2hatk

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  19. Find the work done by a force vecF=4hati+hatj-3hatk, which displace th...

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  20. Constant forces 2hati-5hatj+6hatk and hati+2hatj-hatk act on a particl...

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