Question

1. Consider a vector \underline{A}, written in terms of orthonormal base vectors \underline{i}, \underline{j}, and \underline{k}: \underline{A} = 2\underline{i} - 2\underline{j} + \sqrt{2}\underline{k} Rewrite vector \underline{A} in terms of a new set of orthonormal base vectors \underline{a}, \underline{b}, and \underline{c}, where the angles between the two sets of base vectors are given in the table below: \begin{tabular}{|c|c|c|c|} \hline & \underline{i} & \underline{j} & \underline{k} \\ \hline \underline{a} & 60° & 120° & 135° \\ \hline \underline{b} & 60° & 120° & 45° \\ \hline \underline{c} & 135° & 135° & 90° \\ \hline \end{tabular} For example:

          1. Consider a vector \underline{A}, written in terms of orthonormal base vectors \underline{i}, \underline{j}, and \underline{k}:
\underline{A} = 2\underline{i} - 2\underline{j} + \sqrt{2}\underline{k}
Rewrite vector \underline{A} in terms of a new set of orthonormal base vectors \underline{a}, \underline{b}, and \underline{c}, where the angles between the
two sets of base vectors are given in the table below:
\begin{tabular}{|c|c|c|c|}
\hline
 & \underline{i} & \underline{j} & \underline{k} \\
\hline
\underline{a} & 60° & 120° & 135° \\
\hline
\underline{b} & 60° & 120° & 45° \\
\hline
\underline{c} & 135° & 135° & 90° \\
\hline
\end{tabular}
For example:

1. Consider a vector A, written in terms of orthonormal base vectors i, j, and k:
A = 2i - 2j + √(2)k
Rewrite vector A in terms of a new set of orthonormal base vectors a, b, and c, where the angles between the
two sets of base vectors are given in the table below:

i j k

a 60° 120° 135°

b 60° 120° 45°

c 135° 135° 90°

For example:

Added by James R.

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