Exercises for Question Type 2: Finding the cross product using different operations of vectors

Question 1

Skill question

Let $a = (1, 0, 1)$ , $b = (3, 2, 1)$ , and $c = (5, 6, 1)$ . Compute $(a + b) \times c$ .

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Question 2

Skill question

Let $a = (1, 0, 1)$ , $b = (3, 2, 1)$ , and $c = (5, 6, 1)$ . Compute $(b - c) \times a$ .

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Question 3

Skill question

Let $a = 101$ , $b = 321$ , and $c = 561$ .

Calculate $(2 a + 3 b) \times (b - c)$ .

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Question 4

Skill question

Let $a = (1, 0, 1)$ and $c = (5, 6, 1)$ . Calculate $c \times a$ .

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Question 5

Skill question

Let $a = 101$ , $b = 321$ , and $c = 561$ . Calculate $a \times b$ .

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Question 6

Skill question

Let $a = 101$ , $b = 321$ , and $c = 561$ . Verify the distributive law by simplifying $(a + b) \times (b + c)$ and comparing with $a \times b + a \times c + b \times b + b \times c$ .

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Question 7

Skill question

Let $a = (1, 0, 1)$ , $b = (3, 2, 1)$ , and $c = (5, 6, 1)$ . Compute $b \times c$ .

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Question 8

Skill question

Let $a = (1, 0, 1)$ , $b = (3, 2, 1)$ , and $c = (5, 6, 1)$ . Compute the scalar triple product $a \cdot (b \times c)$ .

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Question 9

Skill question

Let $a = 101$ , $b = 321$ , and $c = 561$ . Calculate $a \times (b + c)$ .

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Question 10

Skill question

Let $a = (1, 0, 1)$ , $b = (3, 2, 1)$ , and $c = (5, 6, 1)$ . Compute $(a \times b) + (b \times c) + (c \times a)$

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Question 11

Skill question

Let $a = 101$ , $b = 321$ , and $c = 561$ . Find a unit vector perpendicular to both $(a + b)$ and $(b + c)$ .

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Question 12

Skill question

Let $a = 101$ , $b = 321$ , and $c = 561$ . Define $u = a + 2 c$ and $v = 3 b - a$ .

Calculate $u \times v$ .

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IB Mathematics Analysis and Approaches Question Type 2: Finding the Cross Product Using Different Operations of Vectors Exercises