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Find the direction cosines of a vector w...

Find the direction cosines of a vector whose direction ratios are (i) 1,2,3, (ii) 3,-1,3 (iii) 0,0,7

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The correct Answer is:
(i) `1/(sqrt(14)),2/(sqrt(14)),3/(sqrt(14))`
(ii) `3//(sqrt(19)),(-1)/(sqrt(19)),3/(sqrt(19))`
(iii) `0/7,0/7,7/7`
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FULL MARKS-VECTOR ALGEBRA-I-EXERCISE 8.2
  1. Verify whether the ratios are direction cosines of some vector or not....

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  2. Find the direction cosines of a vector whose direction ratios are (i) ...

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  3. Find the direction cosines and direction ratios for the following vect...

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  4. A triangle is formed by joining the points (1,0,0), (0,1,0) and (0,0,1...

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  5. If (1)/(2),(1)/(sqrt(2)) a are the direction cosines of some vector, t...

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  6. If (a,a+b,a+b+c) is one set of direction ratios of the line joining (1...

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  7. Show that the vectors -hati-2hatj-6hatk,2hati-hatj+hatk" "and -hati+3h...

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  8. Find the value of lambda for which the vectors veca=3hat(i)+2hat(j)+9h...

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  9. Show that the following vectors are coplaner. (i) hati-2hatj+3hatk,-2...

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  10. Show that the points whose position vectors 4hat(i)+5hatj+hatk,-hatj-h...

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  11. If veca=2hati+3hatj-4hatk,vecb=3hati-4hatj-5hatk, and vecc=-3hati+2hat...

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  12. The position vectors of the vertices of a triangle are hati+2hatj+3hat...

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  13. Find the unit vector parallel to 3veca-2vecb+4vecc,"if"" "veca=3hati-h...

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  14. The position vectors veca,vecb,veccof three points satisfy the relatio...

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  15. The position vectors of the points P,Q,R,S are hati+hatj+hatk,2hati+5h...

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  16. Find the value or values of m for which m (hati+hatj+hatk) is a unit v...

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  17. Show that the points A (1,1,1), B (1,2,3) and C (2,-1,1) are vertices ...

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