Higher Mathematics Vectors Past Papers Unit 3 outcome 1 Written Questions 1. [SQA] 2. [SQA] 3. [SQA] The vectors p , q and r are defined as follows: p = 3 i - 3 j + 2 k , q = 4 i - j + k , r = 4 i - 2 j + 3 k . (a) Find 2 p - q + r in terms of i , j and k . 1 (b) Find the value of |2 p - q + r | . 2 4. [SQA] 5. [SQA] 6. [SQA] 7. [SQA] hsn .uk.net Page 1 Questions marked ‘[SQA]’ c SQA All others c Higher Still Notes
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Vectors Past Papers Unit 3 outcome 1...Vectors Past Papers Unit 3 outcome 1 Written Questions [SQA] 1. PSfrag replacements O x y [SQA] 2. PSfrag replacements O x y [SQA] 3. The vectors
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Higher Mathematics
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Vectors Past Papers Unit 3 outcome 1
Written Questions1.[SQA]
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2.[SQA]PSfrag replacements
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3.[SQA] The vectors p , q and r are defined as follows:
p = 3i − 3 j + 2k , q = 4i − j + k , r = 4i − 2 j + 3k .
28.[SQA] The diagram shows a square-basedpyramid of height 8 units.Square OABC has a side length of 6 units.The coordinates of A and D are (6, 0, 0)and (3, 3, 8) .C lies on the y-axis.(a) Write down the coordinates of B. 1
33.[SQA] A box in the shape of a cuboidis designed with circles of differentsizes on each face.The diagram shows three of thecircles, where the origin representsone of the corners of the cuboid. Thecentres of the circles are A(6, 0, 7) ,B(0, 5, 6) and C(4, 5, 0) .Find the size of angle ABC. 7
40. (a)[SQA] Roadmakers look along the tops of a setof T-rods to ensure that straight sectionsof road are being created. Relative tosuitable axes the top left corners of theT-rods are the points A(−8,−10,−2) ,B(−2,−1, 1) and C(6, 11, 5) .Determine whether or not the section ofroad ABC has been built in a straight line. 3
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(b) A further T-rod is placed such that D hascoordinates (1,−4, 4) .Show that DB is perpendicular to AB. 3PSfrag replacements