Practice Operations On Vectors (5.5) - Vectors

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5 questions

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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Add the vectors $\vec{A} = 1\hat{i} + 2\hat{j}$ and $\vec{B} = 3\hat{i} + 4\hat{j}$ .
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Combine corresponding components.
Question 2.
What happens to a vector when multiplied by a scalar of 0?
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Consider what multiplying by zero does.
3Question 3.
What is the result of the dot product of two perpendicular vectors?
- 1
- 0
- Depends on the vectors
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Think about the relationship of angles between vectors.
4Question 4.
True or false: The cross product of two vectors results in a scalar.
- True
- False
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Consider what you learned about vector products.
Question 5.
Given vectors $\vec{A} = 3\hat{i} + 4\hat{j}\, and \(\vec{B} = 5\hat{i} + 6\hat{j} + 1\hat{k}$ , calculate both their dot and cross products.
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Break it down into component calculations for both products.
Question 6.
A particle is moving along vector $\vec{A} = 50\hat{i} + 100\hat{j}$ and is affected by a force represented by $\vec{B} = -30\hat{i} + 20\hat{j}$ . Calculate the resultant vector and discuss what this vector implies about the particle's new position.
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Use component addition to find the resultant direction.

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