$\"\"$

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(a).

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The points on the plane are $\"\"$ and $\"\"$ .

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The points $\"\"$ are lies on the plane then their vectors $\"\"$ are lie on the same plane.

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If $\"\"$ and $\"\"$ are the two points then the component form of vector $\"\"$ is

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$\"\"$

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$\"\"$

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If $\"\"$ and $\"\"$ are the two points then the component form of vector $\"\"$ is

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$\"\"$

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$\"\"$ .

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The cross product of two vectors produces a vector orthogonal to the two vectors.

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Consider $\"\"$ .

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$\"\"$

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$\"\"$ .

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From geometric properties of the cross product, $\"\"$ is perpendicular to both $\"\"$ and $\"\"$ .

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Thus, $\"\"$ is perpendicular to plane passing through the points $\"\"$ and $\"\"$ .

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$\"\"$

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(b).

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Area of the $\"\"$ is half of the area of the parallelogram with adjacent sides $\"\"$ and $\"\"$ .

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Area of the parallelogram with adjacent sides $\"\"$ and $\"\"$ is $\"\"$ .

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Area of the $\"\"$ is

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$\"\"$

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Area of the $\"\"$ is $\"\"$ sq-units.

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$\"\"$

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$\"\"$ is a non-zero vector perpendicular to plane passing through the points $\"\"$ and $\"\"$ .

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Area of the $\"\"$ is $\"\"$ sq-units.