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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
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    C
    `(2 hat(a) - hat(b))`
    D
    `(2 hat(a) + hat(b))`
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