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vec(P)+vec(Q) is a unit vector along x-a...

`vec(P)+vec(Q)` is a unit vector along x-axis. If `vec(P)= hat(i)-hat(j)+hat(k)`, then what is `vec(Q)`?

A

`hati+hatj-hatk`

B

`hatj-hatk`

C

`hati+hatj+hatk`

D

`hatj+hatk`

Text Solution

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The correct Answer is:
To solve the problem step by step, we need to find the vector \(\vec{Q}\) given that \(\vec{P} + \vec{Q}\) is a unit vector along the x-axis and that \(\vec{P} = \hat{i} - \hat{j} + \hat{k}\). ### Step 1: Understand the given information We know that: - \(\vec{P} + \vec{Q}\) is a unit vector along the x-axis. - A unit vector along the x-axis can be represented as \(\hat{i}\). - \(\vec{P} = \hat{i} - \hat{j} + \hat{k}\). ### Step 2: Set up the equation From the information given, we can write the equation: \[ \vec{P} + \vec{Q} = \hat{i} \] Substituting \(\vec{P}\) into the equation gives: \[ (\hat{i} - \hat{j} + \hat{k}) + \vec{Q} = \hat{i} \] ### Step 3: Rearranging the equation To isolate \(\vec{Q}\), we can rearrange the equation: \[ \vec{Q} = \hat{i} - (\hat{i} - \hat{j} + \hat{k}) \] ### Step 4: Simplifying the expression Now, simplify the right-hand side: \[ \vec{Q} = \hat{i} - \hat{i} + \hat{j} - \hat{k} \] This simplifies to: \[ \vec{Q} = \hat{j} - \hat{k} \] ### Conclusion Thus, the vector \(\vec{Q}\) is: \[ \vec{Q} = \hat{j} - \hat{k} \]
To solve the problem step by step, we need to find the vector \(\vec{Q}\) given that \(\vec{P} + \vec{Q}\) is a unit vector along the x-axis and that \(\vec{P} = \hat{i} - \hat{j} + \hat{k}\). ### Step 1: Understand the given information We know that: - \(\vec{P} + \vec{Q}\) is a unit vector along the x-axis. - A unit vector along the x-axis can be represented as \(\hat{i}\). - \(\vec{P} = \hat{i} - \hat{j} + \hat{k}\). ...
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