JEE Main & Advanced Mathematics Vector Algebra Question Bank Scalar triple product and their applications

  • question_answer
    Let  \[\overrightarrow{A}=i+j+k\], \[\overrightarrow{B}=i,\,\overrightarrow{C}={{C}_{1}}i+{{C}_{2}}j+{{C}_{3}}k\]. If \[{{C}_{2}}=-1\], and \[{{C}_{3}}=1\], then to make three vectors coplanar         [AMU 2000]

    A)             \[{{C}_{1}}=0\]

    B)             \[{{C}_{1}}=1\]

    C)             \[{{C}_{1}}=2\]

    D)             No value of \[{{C}_{1}}\] can be found

    Correct Answer: D

    Solution :

                    To make three vectors coplanar \[[\overrightarrow{A}\,\overrightarrow{B}\,\overrightarrow{C}]=0\]                 The value of \[[\vec{A}\,\vec{B}\,\vec{C}]\] is independent of \[{{C}_{1}}\], hence no value of \[{{C}_{1}}\] can be found.


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