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Hits: 400 Question Relative to an origin , the position vectors of points A and B are and , respectively. i. Use a scalar product to calculate angle BOA. The point C is the mid-point of AB. The point D is such that . ii. Find . Solution i. We recognize that angle BOA is between and . […]
Hits: 349 Question Relative to an origin , the position vectors of points A and B are given by and where is a constant. i. Find the value of for which angle AOB =. ii. In the case where , find the vector which has magnitude 28 and is in the same direction as . Solution i. […]
Hits: 296 Question Relative to an origin , the point A has position vector and the point B has position vector , where is a constant. i. Find . ii. Hence show that there are no real values of for which and are perpendicular to each other. iii. Find the values of for which angle AOB =. Solution i. A […]
Hits: 536 Question In the diagram, OABCDEFG is a rectangular block in which cm and cm. Unit vectors , and are parallel to , and respectively. The point P is the mid-point of DG, Q is the centre of the square face CBFG and R lies on AB such that AR = 4 cm. i. Express each of the […]
Hits: 659 Question Relative to an origin , the position vectors of the points , and are given by and i. Find angle ABC. The point D is such that ABCD is a parallelogram. ii. Find the position vector of D. Solution i. We recognize that angle ABC is between and . Therefore, we need the scalar/dot product of […]
Hits: 900 Question The diagram shows a prism ABCDPQRS with a horizontal square base APSD with sides of length 6 cm. The cross-section ABCD is a trapezium and is such that the vertical edges AB and DC are of lengths 5 cm and 2 cm respectively. Unit vectors , and are parallel to AD, AP and AB respectively. […]