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Vector Algebra question

2015 · Shift 1 · Q35

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PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2015 · Shift 1 · Q35

Vector Algebra question

2015 · Shift 1 · Q35

JEE AdvancedMathematicsVector AlgebraMultiple correct+4 / −1

Let

\Delta PQR

be a triangle. Let

\vec a = \overrightarrow {QR} ,\vec b = \overrightarrow {RP}

and

\overrightarrow c = \overrightarrow {PQ} .

If

\left| {\overrightarrow a } \right| = 12,\,\,\left| {\overrightarrow b } \right| = 4\sqrt 3 ,\,\,\,\overrightarrow b .\overrightarrow c = 24,

then which of the following is (are) true?

A
${{{{\left| {\overrightarrow c } \right|}^2}} \over 2} - \left| {\overrightarrow a } \right| = 12$
B
${{{{\left| {\overrightarrow c } \right|}^2}} \over 2} + \left| {\overrightarrow a } \right| = 30$
C
$\left| {\overrightarrow a \times \overrightarrow b + \overrightarrow c \times \overrightarrow a } \right| = 48\sqrt 3$
D
$\overrightarrow a .\overrightarrow b = - 72$

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