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JEE MATHEMATICS MCQ: CROSS PRODUCT

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Application +4 | -1

\vec{a}=\hat{i}+2 \hat{k}, \vec{b}=\hat{i}+\hat{j}+\hat{k}, \vec{c}=7 \hat{i}-3 \hat{j}+4 \hat{k}

, then the vector

\vec{d}

satisfies the relation

\vec{d} \times \vec{b}=\vec{c} \times \vec{b}, \vec{a} \cdot \vec{d}

=0

is given by

View answer and explanation

Correct option: B

2 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}-\hat{\mathrm{k}}

Option B (

2 \hat{{\mathrm{{i}}}} - 8 \hat{{\mathrm{{j}}}} - \hat{{\mathrm{{k}}}}

) is correct because it satisfies both the conditions

\vec{{d}} \times \vec{{b}} = \vec{{c}} \times \vec{{b}}

and

\vec{{a}} \cdot \vec{{d}} = 0

.

More Questions from CROSS PRODUCT

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A solution of the vector equation

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

\vec{a}, \vec{b}

are two given vectors, is where

\lambda

is a parameter. Let

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

is possible if A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(-1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is Let

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

If c is a vector such that

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

and the angle between

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

is the origin, If

S

is the parallelogram with adjacent sides

O A

O C

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