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Let vec(a) = hat (i) + hat (j) + hat (k...

Let ` vec(a) = hat (i) + hat (j) + hat (k) , vec (b) = hat (i) and vec (c) = c_(1)hat (i) + c_(2)hat (j)+ c_(3)hat(k)` then , if `c_(1)=1 and c_(2) = 2 , ` find `c_(3)` which makes `vec(a),vec(b) and vec(c ) ` coplanar .

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The correct Answer is:
`C_(3)=2`
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CHHAYA PUBLICATION-PRODUCTS OF TWO VECTORS-Exercise 2B ( Short answer type questions)
  1. If vec(a) = hat (i) +hat (j) , vec (b) = hat(i) - hat(j) and vec(c )...

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  2. If vec(alpha ) = hat (i) - 2 hat (j) + 3 hat (k) , vec(beta) = 2 hat ...

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  3. If vec (alpha ) = - hat (i) + 2 hat (j) + hat (k) , vec(b) = 3 hat(i) ...

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  4. The vectors which determine the sides of the parallelopiped are given ...

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  5. The vectors which determine the sides of the parallelopiped are given ...

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  6. In each of the following show that the given vectors are coplanar: ...

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  7. In each of the following show that the given vectors are coplanar: ...

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  8. If vec (a) = -2 hat (i) - 2 hat (j) + 4 hat (k) , vec (b) = - 2 hat(i...

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  9. If the vectors x hat (i) - 4 hat (j) + 5 hat (k) , hat (i) + 2 hat (j...

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  10. If the vectors vec (a) = 2 hat (i) - hat (j) + hat (k) , vec ( b) = h...

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  11. The position vectors of four points A,B,C and D are given below . In e...

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  12. The position vectors of four points A,B,C and D are given below . In e...

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  13. If the vectors -4 hat (i)-6 hat (j) - 2 hat (k) , - hat (i) + 4hat (j)...

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  14. If the vectors vec(a) = 2 hat (i) - lambda hat(j) + 3 hat (k), vec(b)...

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  15. Prove that : (vec(a) + vec(b)). { (vec(b)+vec(c))xx (vec(c)+vec(a))}...

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  16. Prove that : vec(a) . { vec(b) xx (vec(c) + vec(d))} = vec(a) . (ve...

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  17. vec (alpha) = lambda hat (i) + hat (j) + 3 hat (k) , " " vec(beta) = ...

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  18. If the vectors ahat (i) + a hat (j) + c hat (k) , hat (i) + hat (k) an...

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  19. Let vec(a) = hat (i) + hat (j) + hat (k) , vec (b) = hat (i) and vec ...

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  20. Find x such that the four points A(3,2,1), B(4,x,5), C(4,2,-2) and D (...

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