Note: Using with will lead to   0.799. If they then say BO = 0.799, this is a correct solution. calculating = (1)(4) + (2)(6) + (3)(1) (= 19) eg d1•d2 •, evidence of the formula to find the angle cos =  eg = 0.799 radians (accept 45.8) (b) two correct answers (1,  2, 3), (3, 4, 2), (7, 10, 1), (11, 16, 0) eg (c) (i) = r (ii) C on so L2, evidence of equating components 1 3t = 2 + 4t = 5 = 3 + 2t eg  k,  k, one correct value = 1, = (seen anywhere) 2 t k coordinates of C are (2, 2, 5) (d) for setting up one (or more) correct equation using 3 + = 2, 8 2p = 2,  = 5 eg p p =  5 p 4. Solution : evidence of equating vectors (M1) = eg L1 L2 for any two correct equations 2 + = 3 5 + 2s = + 3t, 3 + 3s = 8 4t  3  eg s t, attempting to solve the equations finding correct parameter (s = = 2) one 1, t the coordinates of T are (1, 3, 0) 5. Solution : (a) (i)Evidence of approach = eg (ii) (b) (i) = + or = + r r t t Note: Award A1 if = is missing. “r ” (ii) Evidence of choosing correct vectors , Evidence of calculating magnitudes eg =  36  49 + 100 (= 15) (accept  15) • For evidence of substitution into the correct formula cos  = eg = 1.49 (radians), 85.3  (c) METHOD 1 Geometric approach Valid reasoning
Note: Using with will lead to   0.799. If they then say BO = 0.799, this is a correct solution. calculating •, eg d1•d2 = (1)(4) + (2)(6) + (3)(1) (= 19) evidence of the formula to find the angle eg cos  = = 0.799 radians (accept 45.8) (b) two correct answers eg (1,  2, 3), (3, 4, 2), (7, 10, 1), (11, 16, 0) (c) (i) r = (ii) C on L2, so evidence of equating components eg 1  3t = k,  2 + 4t = k, 5 = 3 + 2t one correct value t = 1, k = 2 (seen anywhere) coordinates of C are (2, 2, 5) (d) for setting up one (or more) correct equation using eg 3 + p = 2, 8 2p = 2,  p = 5 p =  5 4. Solution : evidence of equating vectors (M1) eg L1 = L2 for any two correct equations eg 2 + s = 3  t, 5 + 2s = 3 + 3t, 3 + 3s = 8  4t attempting to solve the equations finding one correct parameter (s = 1, t = 2) the coordinates of T are (1, 3, 0) 5. Solution : (a) (i)Evidence of approach eg = (ii) (b) (i) r = + t or r = + t Note: Award A1 if “r = ” is missing. (ii) Evidence of choosing correct vectors , Evidence of calculating magnitudes eg • =  36  49 + 100 (= 15) (accept  15) For evidence of substitution into the correct formula eg cos  =  = 1.49 (radians), 85.3 (c) METHOD 1 Geometric approach Valid reasoning
topic_4_vectors_review_markscheme.docx