Date | May 2019 | Marks available | 7 | Reference code | 19M.1.SL.TZ1.S_6 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 1 |
Command term | Find | Question number | S_6 | Adapted from | N/A |
Question
The magnitudes of two vectors, u and v, are 4 and respectively. The angle between u and v is .
Let w = u − v. Find the magnitude of w.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
METHOD 1 (cosine rule)
diagram including u, v and included angle of (M1)
eg
sketch of triangle with w (does not need to be to scale) (A1)
eg
choosing cosine rule (M1)
eg
correct substitution A1
eg
(seen anywhere) (A1)
correct working (A1)
eg 16 + 3 − 12
| w | = A1 N2
METHOD 2 (scalar product)
valid approach, in terms of u and v (seen anywhere) (M1)
eg | w |2 = (u − v)•(u − v), | w |2 = u•u − 2u•v + v•v, | w |2 = ,
| w | =
correct value for u•u (seen anywhere) (A1)
eg | u |2 = 16, u•u = 16,
correct value for v•v (seen anywhere) (A1)
eg | v |2 = 16, v•v = 3,
(seen anywhere) (A1)
u•v (= 6) (seen anywhere) A1
correct substitution into u•u − 2u•v + v•v or (2 or 3 dimensions) (A1)
eg 16 − 2(6) + 3 (= 7)
| w | = A1 N2