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If vec aand vec bare two collinear ve...

If ` vec a`and ` vec b`are two collinear vectors, then which of the following are incorrect:(A) ` vec b=lambda vec a ,`for some scalar lambda (B) ` vec a=+- vec b` (C) the respective components of ` vec a`and ` vec b`are proportional (D) both the vectors `vec a` and `vec b ` have same direction, but different magnitudes.

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To solve the problem, we need to analyze the properties of collinear vectors and determine which of the given options is incorrect. ### Step-by-Step Solution: 1. **Understanding Collinear Vectors**: - Two vectors \(\vec{a}\) and \(\vec{b}\) are said to be collinear if they lie along the same line. This means that one vector can be expressed as a scalar multiple of the other. Mathematically, this can be expressed as: \[ \vec{a} = \lambda \vec{b} ...
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Knowledge Check

  • If vec(a) and vec(b) are two unit vectors, then the vector (vec(a) + vec(b)) xx (vec(a) xx vec(b)) is parallel to

    A
    `(hat(a)- hat(b))`
    B
    `(hat(a)+ hat(b))`
    C
    `(2 hat(a) - hat(b))`
    D
    `(2 hat(a) + hat(b))`
  • NCERT-VECTOR ALGEBRA-EXERCISE 10.2
    1. If vec aand vec bare two collinear vectors, then which of the foll...

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    2. In triangle ABC (Figure), which of the following is not true: (A) v...

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    3. Show that the vectors 2 hat i-3 hat j+4 hat kand -4 hat i+6 hat j-8 h...

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    4. Find a vector in the direction of vector 5 hat i- hat j+2 hat kwhich ...

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    5. Find the direction cosines of the vector joining the points A(1, 2, 3...

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    6. Find the direction cosines of the vector hat i+2 hat j+3 hat k.

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    7. Find the position vector of a point R which divides the line joining ...

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    8. Show that the vector hat i+ hat j+ hat kis equally inclined to the a...

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    9. Show that the points A, B and C with position vectors, veca=3 hat i-...

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    10. Find the position vector of the mid point of the vector joining the p...

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    11. Find the unit vector in the direction of vector vec(PQ), where P an...

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    12. For given vectors, veca=2 hat i- hat j+2 hat k and vecb=- hat i+ ha...

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    13. Write two different vectors having same magnitude.

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    14. Write two different vectors having same direction.

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    15. Compute the magnitude of the following vectors: vec a= hat i+ hat j+ ...

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    16. Find the sum of the vectors veca= hat i-2 hat j+ hat k , vecb=-2 hat...

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    17. Find the unit vector in the direction of the vector veca= hat i+ ha...

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    18. Find the values of x and y so that the vectors 2 hat i+3 hat jand x h...

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    19. Find the scalar and vector components of the vector with initial poin...

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