ECAT Mathematics — Vectors
Vectors is part of the Mathematics section of the UET ECAT (30 of the 100 MCQs). It breaks into 4 subtopics, and we hold 20 ECAT-pattern practice MCQs on it, each with a written explanation. Tap a subtopic below to practise just that.
Subtopics (4)
How Vectors is tested
Across the 7 ECAT past papers on ParhaiKrlo, Vectors accounts for 4 questions. It appears in 3 of them, about 1.3 questions a paper. The heaviest was ECAT Past Paper 07, with 2 questions.
| Paper | Questions |
|---|---|
| ECAT Past Paper 07 | 2 |
| ECAT Past Paper 05 | 1 |
| ECAT Past Paper 02 | 1 |
Vectors MCQs from the ECAT past papers
Try each one before opening the answer. Each comes with a short explanation.
- Q1 · ECAT Past Paper 07 · Vectors
Vectors u = a i − j + k and v = i − 2j + b k are collinear if:
- A.a = 1, b = 1
- B.a = 1/2, b = 2
- C.a = 2, b = 1/2
- D.a = −1, b = −1
Show answer
Answer: B. a = 1/2, b = 2 — u = λv: −1 = −2λ gives λ = 1/2, so a = 1/2 and 1 = b/2, b = 2.
- Q2 · ECAT Past Paper 05 · Vectors
The projection of a = −2i + 3j + 7k on b = 2j + k is:
- A.13/5
- B.13/4
- C.13/√5
- D.13
Show answer
Answer: C. 13/√5 — Projection = a·b/|b| = (6 + 7)/√5 = 13/√5.
- Q3 · ECAT Past Paper 02 · Vectors
If a = 7i + 2j − k and b = 4i + 2j + 3k, then a × b = ?
- A.8i + 25j + 6k
- B.−8i − 25j + 6k
- C.6i − 25j + 8k
- D.8i − 25j + 6k
Show answer
Answer: D. 8i − 25j + 6k — a × b = (2·3 − (−1)·2)i − (7·3 − (−1)·4)j + (7·2 − 2·4)k = 8i − 25j + 6k.