Question:
In a vector \(\vec{p}\), 'x' and 'y' components have magnitudes 2 units and 5 units respectively. A vector \(\vec{q}\), along negative Y axis has magnitude of 3 units. Then \(\vec{p}\cdot \vec{q}\) is
In a vector \(\vec{p}\), 'x' and 'y' components have magnitudes 2 units and 5 units respectively. A vector \(\vec{q}\), along negative Y axis has magnitude of 3 units. Then \(\vec{p}\cdot \vec{q}\) is
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The dot product multiplies matching components and adds them. Vector q has only a Y component.
Updated On: Nov 12, 2026
- \(-6\)
- \(-9\)
- \(-10\)
- \(-15\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
The dot product of two vectors is the sum of the products of their matching components.
\(\vec{p}\cdot\vec{q}=p_xq_x+p_yq_y\)
Step 2: Write the Components
\(\vec{p}=2\hat{i}+5\hat{j}\)
Since \(\vec{q}\) points along the negative Y axis, \(\vec{q}=-3\hat{j}\).
Step 3: Calculation
\(\vec{p}\cdot\vec{q}=(2)(0)+(5)(-3)=-15\)
Step 4: Compare the options
The value \(-15\) matches the last option.
Final Answer:
The dot product of the two vectors is -15. \[ \boxed{\text{(D) }-15} \]
The dot product of two vectors is the sum of the products of their matching components.
\(\vec{p}\cdot\vec{q}=p_xq_x+p_yq_y\)
Step 2: Write the Components
\(\vec{p}=2\hat{i}+5\hat{j}\)
Since \(\vec{q}\) points along the negative Y axis, \(\vec{q}=-3\hat{j}\).
Step 3: Calculation
\(\vec{p}\cdot\vec{q}=(2)(0)+(5)(-3)=-15\)
Step 4: Compare the options
The value \(-15\) matches the last option.
Final Answer:
The dot product of the two vectors is -15. \[ \boxed{\text{(D) }-15} \]
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