JEE MATHEMATICS MCQ: CROSS PRODUCT

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Analyzing +4 | -1

Let a unit vector

\widehat{O P}

makes angles

\alpha, \beta, \gamma

with the positive directions of the co-ordinate axes

O X, O Y

O Z

respectively, where

\beta \in\left(0, \frac{\pi}{2}\right)

. If

\widehat{O P}

is perpendicular to the plane through points

(1,2,3)

(2,3,4)

and

(1,5,7)

, then which one of the following is true?

View answer and explanation

Correct option: C

\alpha \in\left(\frac{\pi}{2}, \pi\right)

and

\gamma \in\left(\frac{\pi}{2}, \pi\right)

Option C is correct because the direction cosines are determined from the normal vector to the plane, leading to angles in the specified quadrants.

More Questions from CROSS PRODUCT

Practice All Chapter MCQs →

\vec{r} \times \vec{b}=\vec{a} \times \vec{b}

\vec{a}, \vec{b}

\lambda

a = 3\hat i + 2\hat j + x\hat k\mathrm{ }\,\mathrm{\,\,and}\,\,\mathrm{ }b = \hat i - \hat j + \hat k

x.

\left| {a \times b} \right| = r

a = 2\widehat i + \widehat j - 2\widehat k{\text{ }}\,\,{\text{and }}\,\,b = \widehat i + \widehat j.

a \cdot c = |c|,\,\,|c - a\mid = 2\sqrt 2

a \times b

c

30^\circ ,

|(a \times b) \times c|

\vec{A}=i-2 j-3 k, \vec{B}=2 i+j-k, \vec{C}=i+3 j-2 k

(\vec{A} \times \vec{B}) \times \vec{C}

\overrightarrow{O A}=\vec{a}, \overrightarrow{O B}=12 \vec{a}+4 \vec{b}

O

S

O A

O C

\frac{\text { area of the quadrilateral } O A B C}{\text { area of } S}