If `vecA=2hati-3hatj+4hatk`, its components in YZ-plane and ZX-plane are respectively

Options

A. `sqrt(13)` and 5
B. 5 and `2sqrt(5)`
C. `2sqrt(5)` and `sqrt(13)`
D. `sqrt(13)` and `sqrt(29)`

Explanation

To find the components of the vector \(\vec{A} = 2\hat{i} - 3\hat{j} + 4\hat{k}\) in the YZ-plane and ZX-plane, we can follow these steps:

### Step 1: Understand the planes
- The **YZ-plane** is defined by the axes \(\hat{j}\) and \(\hat{k}\), meaning that the \(x\) component is zero in this plane.
- The **ZX-plane** is defined by the axes \(\hat{i}\) and \(\hat{k}\), meaning that the \(y\) component is zero in this plane.

### Step 2: Find the component in the YZ-plane
To find the component of vector \(\vec{A}\) in the YZ-plane, we ignore the \(x\) component:
\[ \vec{A}_{YZ} = 0\hat{i} - 3\hat{j} + 4\hat{k} \]
The magnitude of this component can be calculated using:
\[ |\vec{A}_{YZ}| = \sqrt{(-3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

### Step 3: Find the component in the ZX-plane
To find the component of vector \(\vec{A}\) in the ZX-plane, we ignore the \(y\) component:
\[ \vec{A}_{ZX} = 2\hat{i} + 0\hat{j} + 4\hat{k} \]
The magnitude of this component can be calculated using:
\[ |\vec{A}_{ZX}| = \sqrt{(2)^2 + (4)^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5} \]

### Final Answer
Thus, the components of the vector \(\vec{A}\) in the YZ-plane and ZX-plane are:
- YZ-plane: \(5\)
- ZX-plane: \(2\sqrt{5}\)