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Consider the following two statements: Statement 1: If A, B and C are points with position vectors \(\vec a = 2\hat i + \hat j + \hat k\), \(\vec b = 3\hat i - \hat j + 3\hat k\) and \(\vec c = \hat i + 7\hat j - 5\hat k\), then the figure OABC forms a tetrahedron. Statement 2: If the position vectors \(\vec a\), \(\vec b\) and \(\vec c\) of points A, B and C are non-coplanar, then OABC is a tetrahedron, where O denotes the origin. Choose the correct option.

1. Statement 1 is true, Statement 2 is true, and Statement 2 correctly explains Statement 1
2. Statement 1 is true, Statement 2 is true, but Statement 2 does not correctly explain Statement 1
3. Statement 1 is false, Statement 2 is true
4. Statement 1 is true, Statement 2 is false

Correct answer: Statement 1 is false, Statement 2 is true

Solution

Statement 1 is false because the given points A, B, and C are coplanar, which means they do not form a tetrahedron with the origin O. Statement 2 is true as it correctly states that non-coplanar points A, B, and C along with the origin O will indeed form a tetrahedron.

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