Question

Find \[x\], \[y\], and \[z\] so that \[\vec{a}=x\hat{i}+2\hat{j}+z\hat{k}\] and \[\vec{b}=2\hat{i}+y\hat{j}+\hat{k}\] are equal.

Options

• \[x=1,\ y=2,\ z=2\]

• \[x=2,\ y=2,\ z=1\]

• \[x=2,\ y=2,\ z=2\]

• \[x=2,\ y=1,\ z=2\]

Answer 1

For equal vectors, corresponding components must be equal. Comparing the \[\hat{i}\], \[\hat{j}\], and \[\hat{k}\] components gives \[x=2\], \[y=2\], and \[z=1\].