A unit vector making an obtuse angle with x - axis and perpendicular to the plane containing the points -2 -3 k- 2 -3 -4 k- and -5 -7 k-A- Also makes and obtuse angle with y - axisB- Also makes an obtuse angle with z - axisC- Also makes an obtuse angle with y and z axisD- None of the above

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Applications of Cross Product

A unit vector...

Question

A unit vector making an obtuse angle with x – axis and perpendicular to the plane containing the points $^i - 2^j + 3^k, 2^i - 3^j + 4^k$ and $^i - 5^j + 7^k$ ,

Also makes and obtuse angle with y - axis

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Also makes an obtuse angle with z - axis

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Also makes an obtuse angle with y and z axis

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None of the above

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Solution

The correct option is B Also makes an obtuse angle with z - axis
Let the given points be A, B and C respectively. The unit vectors perpendicular to the plane containing A, B and C are given by
$\pm \frac{- - \to A B \times - - \to A C}{| - - \to A B \times - - \to A C |} = \pm \frac{1}{\sqrt{26}} (^i - 4^j + 3^k)$
Since the required vector makes an obtuse angle with x – axis. So, it is equal to $\frac{- 1}{\sqrt{26}} (^i - 4^j + 3^k)$ . Clearly it also makes an obtuse angle with z - axis.

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A unit vector making an obtuse angle with x – axis and perpendicular to the plane containing the points ^i−2^j+3^k,2^i−3^j+4^k and ^i−5^j+7^k,

A unit vector making an obtuse angle with x – axis and perpendicular to the plane containing the points $^i - 2^j + 3^k, 2^i - 3^j + 4^k$ and $^i - 5^j + 7^k$ ,