jee-advanced 2015 Q58

jee-advanced · India · paper1 Vectors Introduction & 2D True/False or Multiple-Statement Verification

Let $\triangle P Q R$ be a triangle. Let $\vec { a } = \overrightarrow { Q R } , \vec { b } = \overrightarrow { R P }$ and $\vec { c } = \overrightarrow { P Q }$. If $| \vec { a } | = 12 , | \vec { b } | = 4 \sqrt { 3 }$ and $\vec { b } \cdot \vec { c } = 24$, then which of the following is (are) true?
(A) $\frac { | \vec { c } | ^ { 2 } } { 2 } - | \vec { a } | = 12$
(B) $\frac { | \vec { c } | ^ { 2 } } { 2 } + | \vec { a } | = 30$
(C) $| \vec { a } \times \vec { b } + \vec { c } \times \vec { a } | = 48 \sqrt { 3 }$
(D) $\vec { a } \cdot \vec { b } = - 72$

Let $\triangle P Q R$ be a triangle. Let $\vec { a } = \overrightarrow { Q R } , \vec { b } = \overrightarrow { R P }$ and $\vec { c } = \overrightarrow { P Q }$. If $| \vec { a } | = 12 , | \vec { b } | = 4 \sqrt { 3 }$ and $\vec { b } \cdot \vec { c } = 24$, then which of the following is (are) true?\\
(A) $\frac { | \vec { c } | ^ { 2 } } { 2 } - | \vec { a } | = 12$\\
(B) $\frac { | \vec { c } | ^ { 2 } } { 2 } + | \vec { a } | = 30$\\
(C) $| \vec { a } \times \vec { b } + \vec { c } \times \vec { a } | = 48 \sqrt { 3 }$\\
(D) $\vec { a } \cdot \vec { b } = - 72$

Paper Questions

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