Consider the vectors \(\vec{A}=\hat{i}+\hat{j}-\hat{k}, \vec{B}=2 \hat{i}-\hat{j}+\hat{k}, \vec{C}=\frac{1}{\sqrt{5}}(\hat{i}-2 \hat{j}+2 \hat{k})\). What is the value of \(\vec{C} \cdot(\vec{A} \times \vec{B}) ?\)

Question

Consider the vectors \(\vec{A}=\hat{i}+\hat{j}-\hat{k}, \vec{B}=2 \hat{i}-\hat{j}+\hat{k}, \vec{C}=\frac{1}{\sqrt{5}}(\hat{i}-2 \hat{j}+2 \hat{k})\). What is the value of \(\vec{C} \cdot(\vec{A} \times \vec{B}) ?\)

3 Answers

kritika · Answer 1 · 2021-12-16T09:03:21+0000

Ans( B)

\overrightarrow{\mathrm{C}} .(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}})=\left|\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

Consider the vectors \(\vec{A}=\hat{i}+\hat{j}-\hat{k}, \vec{B}=2 \hat{i}-\hat{j}+\hat{k}, \vec{C}=\frac{1}{\sqrt{5}}(\hat{i}-2 \hat{j}+2 \hat{k})\). What is the value of \(\vec{C} \cdot(\vec{A} \times \vec{B}) ?\)

Your answer

3 Answers

Your comment on this answer:

Your comment on this answer:

Your comment on this answer:

Related questions

Categories