Exercises for Question Type 5: Visually representing vector operations

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Exercises for Question Type 5: Visually representing vector operations - IB

Question 1

Given a = 113, b = 10 - 1 and c = 111, find the vector a + b - c .

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Question 2

Given a = (1, 1, 3), b = (1, 0, - 1) and c = (1, 1, 1), calculate the scalar triple product a \cdot (b \times c) and interpret its absolute value geometrically.

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Question 3

Given a = 113, b = 10 - 1 and c = 111, compute the vector b - a + c .

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Question 4

Given a = 113, b = 10 - 1 and c = 111, find the magnitude of the vector a + b + \frac{1}{2} c .

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Question 5

Given a = (1, 1, 3), b = (1, 0, - 1) and c = (1, 1, 1), find the vector that goes from the point represented by b to the point represented by a + c .

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Question 6

Given a = (1, 1, 3), b = (1, 0, - 1) and c = (1, 1, 1), find the magnitude of the vector - 2 (a + b + c) .

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Question 7

Given a = (1, 1, 3), b = (1, 0, - 1) and c = (1, 1, 1), find 2 a - b + 3 c .

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Question 8

Given b = 10 - 1 and c = 111, compute the projection of b onto c .

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Question 9

This question assesses the ability to perform scalar multiplication of vectors, vector addition, and apply the midpoint formula in three-dimensional space.

Given a = (1, 1, 3), b = (1, 0, - 1) and c = (1, 1, 1), find the midpoint of the segment joining the points represented by b and 2 c .

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Question 10

Given a = (1, 1, 3), b = (1, 0, - 1) and c = (1, 1, 1), calculate the distance between the points represented by u = a + b + \frac{1}{2} c and v = - 2 (a + b + c) .

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Question 11

Given a = (1, 1, 3), b = (1, 0, - 1) and c = (1, 1, 1), find a unit vector in the direction of a + b - c .

Given a = (1, 1, 3), b = (1, 0, - 1) and c = (1, 1, 1), find a unit vector in the direction of a + b - c .

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Question 12

Given a = 113, b = 10 - 1 and c = 111, compute (a + b) - (b + c) .

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IB Mathematics Applications & Interpretation Question Type 5: Visually Representing Vector Operations Exercises