Tip:A–D to answerE for explanationV for videoS to reveal answer
Let a=i+2j+k, b=3(i^−j^+k^). Let c be the vector such that a×c=b and a⋅c=3. Then a((c×b)−b−c) is equal to :
- A.
20
- B.
24
(Correct Answer) - C.
36
- D.
32
Explanation
\begin{aligned}
& \mathrm{Given},\vec{a}=\hat{i}+2\hat{j}+\hat{k};\vec{b}=3(\hat{i}-\hat{j}+\hat{k}) \\
& \vec{a}\left((\vec{c}\times\vec{b})-\vec{b}-\vec{c}\right)=\vec{a}.(\vec{c}\times\vec{b})-\vec{a}.\vec{b}-\vec{a}.\vec{c} \\
& =(\vec{a}\times\vec{c}).\vec{b}-((1)(3)+(2)(3)+(1)(3))-(3) \\
& =\vec{b}.\vec{b}-0-3(9+9+9)-23=24
\end{aligned}
Explanation
\begin{aligned}
& \mathrm{Given},\vec{a}=\hat{i}+2\hat{j}+\hat{k};\vec{b}=3(\hat{i}-\hat{j}+\hat{k}) \\
& \vec{a}\left((\vec{c}\times\vec{b})-\vec{b}-\vec{c}\right)=\vec{a}.(\vec{c}\times\vec{b})-\vec{a}.\vec{b}-\vec{a}.\vec{c} \\
& =(\vec{a}\times\vec{c}).\vec{b}-((1)(3)+(2)(3)+(1)(3))-(3) \\
& =\vec{b}.\vec{b}-0-3(9+9+9)-23=24
\end{aligned}
