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If A = 2i - 3j + 4k, its component in xy...

If A = 2i - 3j + 4k, its component in xy plane is

A

4

B

`sqrt(13)`

C

`sqrt(29)`

D

1

Text Solution

AI Generated Solution

The correct Answer is:
To find the component of the vector \( \mathbf{A} = 2\mathbf{i} - 3\mathbf{j} + 4\mathbf{k} \) in the xy-plane, we can follow these steps: ### Step 1: Identify the components of the vector The vector \( \mathbf{A} \) has three components: - \( \mathbf{i} \) component: 2 - \( \mathbf{j} \) component: -3 - \( \mathbf{k} \) component: 4 ### Step 2: Understand the xy-plane In the xy-plane, we only consider the components of the vector that lie in that plane. This means we will only take the \( \mathbf{i} \) and \( \mathbf{j} \) components and ignore the \( \mathbf{k} \) component. ### Step 3: Write the vector in the xy-plane Thus, the component of vector \( \mathbf{A} \) in the xy-plane is: \[ \mathbf{A}_{xy} = 2\mathbf{i} - 3\mathbf{j} \] ### Step 4: Calculate the magnitude of the vector in the xy-plane To find the magnitude of the vector \( \mathbf{A}_{xy} \), we use the formula for the magnitude of a vector: \[ |\mathbf{A}_{xy}| = \sqrt{(2)^2 + (-3)^2} \] ### Step 5: Simplify the expression Calculating the squares: \[ |\mathbf{A}_{xy}| = \sqrt{4 + 9} = \sqrt{13} \] ### Final Answer The magnitude of the component of vector \( \mathbf{A} \) in the xy-plane is \( \sqrt{13} \). ---
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