Question:
The area of rectangle with sides as \(\vec A=3\hat i+4\hat j\) and \(\vec B=\hat i+3\hat j\) is
The area of rectangle with sides as \(\vec A=3\hat i+4\hat j\) and \(\vec B=\hat i+3\hat j\) is
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Area of a rectangle is product of the lengths of its two adjacent sides.
Updated On: May 7, 2026
- \(5\sqrt{10}\) units
- \(10\) units
- \(2\sqrt{10}\) units
- \(10\sqrt5\) units
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The Correct Option is A
Solution and Explanation
Concept:
If two adjacent sides of a rectangle are represented by vectors, the area can be calculated using the product of magnitudes when the sides are perpendicular.
Step 1: Given: \[ \vec A=3\hat i+4\hat j \] and \[ \vec B=\hat i+3\hat j \]
Step 2: Magnitude of \(\vec A\): \[ |\vec A|=\sqrt{3^2+4^2} \] \[ |\vec A|=\sqrt{9+16}=5 \]
Step 3: Magnitude of \(\vec B\): \[ |\vec B|=\sqrt{1^2+3^2} \] \[ |\vec B|=\sqrt{1+9}=\sqrt{10} \]
Step 4: Area of rectangle: \[ \text{Area}=|\vec A|\cdot|\vec B| \] \[ =5\sqrt{10} \] \[ \boxed{5\sqrt{10}\text{ units}} \]
If two adjacent sides of a rectangle are represented by vectors, the area can be calculated using the product of magnitudes when the sides are perpendicular.
Step 1: Given: \[ \vec A=3\hat i+4\hat j \] and \[ \vec B=\hat i+3\hat j \]
Step 2: Magnitude of \(\vec A\): \[ |\vec A|=\sqrt{3^2+4^2} \] \[ |\vec A|=\sqrt{9+16}=5 \]
Step 3: Magnitude of \(\vec B\): \[ |\vec B|=\sqrt{1^2+3^2} \] \[ |\vec B|=\sqrt{1+9}=\sqrt{10} \]
Step 4: Area of rectangle: \[ \text{Area}=|\vec A|\cdot|\vec B| \] \[ =5\sqrt{10} \] \[ \boxed{5\sqrt{10}\text{ units}} \]
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