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QLDSpecialist MathematicsQuick questions

Unit 3: Mathematical induction, and further vectors, matrices and complex numbers

Quick questions on Vectors in three dimensions, dot and cross products (QCE Specialist Mathematics Unit 3)

6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the dot (scalar) product?
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The dot product produces a scalar:
What is the cross (vector) product?
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The cross product produces a vector perpendicular to both inputs:
What are equations of lines?
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A line through point AA with position vector a\mathbf{a} and direction d\mathbf{d} has vector equation
What is dot product?
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a⋅b=(2)(1)+(−1)(3)+(2)(−1)=2−3−2=−3.\mathbf{a}\cdot\mathbf{b} = (2)(1) + (-1)(3) + (2)(-1) = 2 - 3 - 2 = -3.
What are magnitudes?
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∣a∣=4+1+4=9=3.|\mathbf{a}| = \sqrt{4+1+4} = \sqrt{9} = 3. ∣b∣=1+9+1=11.\quad |\mathbf{b}| = \sqrt{1+9+1} = \sqrt{11}.
What is check?
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(a×b)⋅a=−10−4+14=0(\mathbf{a}\times\mathbf{b})\cdot\mathbf{a} = -10 - 4 + 14 = 0, confirming perpendicularity.

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