Practice Dot Product (scalar Product) (5.5.4) - Vectors - ICSE 12 Mathematics

Practice: Dot Product (Scalar Product)

Lesson 5.5.4Vectors

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9 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the dot product of $\vec{A} = (1, 2)$ and $\vec{B} = (3, 4)$ ?
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Use the formula \$ A_xB_x + A_yB_y \$.
Question 2.
Is the result of a dot product a vector or a scalar?
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Think about what kind of quantity a dot product yields.
3Question 3.
What does the dot product yield?
- A vector
- A matrix
- A scalar
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Remember, it gives a number, not a direction.
4Question 4.
If $\vec{A} \cdot \vec{A} = 0$ , what can be said about $\vec{A}$ ?
- True
- False
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Think about vectors and their magnitudes.
Question 5.
Given two vectors, $\vec{A} = (2, 3, 4)$ and $\vec{B} = (-1, 0, 5)$ , find $\vec{A} \cdot \vec{B}$ and interpret the result in terms of direction.
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Apply the dot product formula and sum the results carefully.
Question 6.
If $|\vec{A}| = 5$ and $|\vec{B}| = 12$ with an angle of $60^\circ$ between them, calculate $\vec{A} \cdot \vec{B}$
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Use the cosine value and multiply it with the magnitudes.

5 more questions in this section. Enroll free to practise them all.