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

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

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 following vectors are coplanar : 3hati-2hatj+4hatk,6hati+3hatj+2hatk . 5hati+7hatj+3hatk . 2hati+2hatj+5hatk .

Show that the following vectors are collinear : 2hati-3hatj+4hatk and -4hati+6hatj-8hatk .

Using scalar triple product, show that the four points given by position vectors hati+hatj+10hatk , 2hati+3hatj+11hatk , 3hati+2hatj+6hatk and hati-2hatj+4hatk are coplanar.

Show that the three points with position vectors 2hati+6hatj+3hatk , hati+2hatj+7hatk and 3hati+10hatj-hatk are collinear.

Show that the three points with position vectors hati+2hatj+7hatk , 2hati+6hatj+3hatk and 3hati+10hatj-hatk are collinear.

Show that the following vectors are coplanar : hati-hatj+hatk,6hati-hatk and 4hati+2hatj-3hatk .

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

PSEB-VECTOR ALGEBRA-Exercise
  1. Find the projection of the vector veci + 3vecj + 7veck on the vector ...

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

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

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  4. Show that the given vector is a unit vector: (1/7)(6veci + 2vecj - 3v...

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

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  6. Evaluate the product (3 hata-5hatb) cdot(2hata+7hatb)

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  7. Find the magnitude of two vectors veca and vecb, having the same magni...

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  8. Find |vecx|, if for a unit vector veca, (vecx - veca)cdot(vecx+veca)...

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  9. If veca = 2veci + 2vecj + 3veck, vecb = -veci + 2vecj + veck and vecc ...

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

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  11. If veca cdot veca = 0 and veca cdot vecab = 0, then what can be concl...

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

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  13. If either vector veca = 0or vecb = 0, then veca cdot vecb = 0.But the...

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

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

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  16. Show that the points A(2veci-vecj+veck), B(veci-3vecj-5veck), C(3veci-...

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  17. If veca is a nonzero vector of magnitude 'a' and lambda a nonzero s...

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  18. Find |vecaxxvecb|, if veca = veci - 7vecj + 7veck and vecb = 3veci - 2...

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  19. Find a unit vector perpendicular to each of the vector veca + vecb and...

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  20. If a unit vector veca, makes angles pi/3with hati, pi/4wih hatj and...

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