P4.7 - Vectors

Vectors in two and three dimensions.

Use vectors in two and three dimensions to connect the rule to the data and decision in the question.

This matters because vectors in two and three dimensions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply vectors in two and three dimensions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Vectors in two and three dimensions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Magnitude of a vector.; Students should be able to find a unit vector in the direction of a, and be familiar with | a |.

Use magnitude of a vector to connect the rule to the data and decision in the question.

This matters because magnitude of a vector determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply magnitude of a vector to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Magnitude of a vector is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Perform vector addition and scalar multiplication and interpret both operations geometrically.

Use vector addition and scalar multiplication to connect the rule to the data and decision in the question.

This matters because vector addition and scalar multiplication determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply vector addition and scalar multiplication to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Vector addition and scalar multiplication is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Position vectors.; OB − OA = AB = b − a.

Use position vectors to connect the rule to the data and decision in the question.

This matters because position vectors determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply position vectors to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Position vectors is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The distance between two points.; The distance d between two points (x, y, z) and (x, y, z) is given by 1 1 1 2 2 2 d 2 = (x – x)2 + (y – y)2 + (z – z)2 1 2 1 2 1 2.

Use distance between two points to connect the rule to the data and decision in the question.

This matters because distance between two points determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply distance between two points to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: distance between two points is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Vector equations of lines.; To include the forms r = a + tb and r = c + t(d – c) Conditions for two lines to be parallel, intersecting or skew.

Use vector equations of lines to connect the rule to the data and decision in the question.

This matters because vector equations of lines determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply vector equations of lines to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.

Use the scalar product a·b = a1b1 + a2b2 + a3b3 and a·b = |a||b| cos θ to calculate angles between lines and identify perpendicular non-zero vectors.

Use scalar product to connect the rule to the data and decision in the question.

This matters because scalar product determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply scalar product to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Scalar product is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.