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Vector Algebra question

2002 · Shift 0 · Q90

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PYQ Library
JEE Main
Mathematics
Vector Algebra
2002 · Shift 0 · Q90

Vector Algebra question

2002 · Shift 0 · Q90

JEE MainMathematicsVector AlgebraMCQ+4 / −1

If the vectors

\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{b}}

and

\overrightarrow{\mathbf{c}}

from the sides

B C, C A

and

A B

respectively of a triangle

A B C

, then :

A
$\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}=\overrightarrow{\mathbf{b}} \cdot \overrightarrow{\mathbf{c}}=\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathbf{b}}=0$
B
$\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}=\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}=\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}$
C
$\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathbf{b}}=\overrightarrow{\mathbf{b}} \cdot \overrightarrow{\mathbf{c}}=\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathbf{a}}=0$
D
$\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}=\overrightarrow{\mathbf{0}}$

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