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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

Consider the vectors A = i + j - k , B =2 i - j + k , C = 1 5 ( i...

Consider the vectors A→=i^+j^−k^,B→=2i^−j^+k^,C→=15(i^−2j^+2k^)\overrightarrow{\mathrm{A}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}, \overrightarrow{\mathrm{B}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overrightarrow{\mathrm{C}}=\frac{1}{\sqrt{5}}(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}). What is the value of C→.(A→×B→)?\overrightarrow{\mathrm{C}} .(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}) ?

Options

  1. A1
  2. B0
  3. C323 \sqrt{2}
  4. D18518 \sqrt{5}

Correct answer

B. 0

Step-by-step solution

Hint: \overrightarrow{\mathrm{C}}(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}})=\left|11−12−111−22\begin{array}{ccc}1 & 1 & -1 \\ 2 & -1 & 1 \\ 1 & -2 & 2\end{array}\right|=1(-2+2)-1(4-1)-1(-4+1)=-3+3=0
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