Let u, v, w be such that |u|=1, |v|=2, |w|=3. If the projection v along u is equal to that of w along u and v, w are perpendicular to each other then - Mathematics MCQ AIEEE 2004 2026 | ExamTest.live

hardMCQAIEEE 20042026Mathematics

1 attempts0% success rate3 marks (−1)

Let u, v, w be such that ∣ u ∣ = 1, ∣ v ∣ = 2, ∣ w ∣ = 3. If the projection v along u is equal to that of w along u and v, w are perpendicular to each other then ∣ u - v + w ∣ equals

Solution & Step-by-step Explanation

Given: ∣ u ∣ = 1, ∣ v ∣ = 2, ∣ w ∣ = 3 .Projection of v on u is \frac{v \cdot u}{∣ u ∣} . Projection of w on u is \frac{w \cdot u}{∣ u ∣} . So, v \cdot u = w \cdot u . v, w are perpendicular \Rightarrow v \cdot w = 0 .Calculate ∣ u - v + w ∣^{2} : ∣ u - v + w ∣^{2} = ∣ u ∣^{2} + ∣ v ∣^{2} + ∣ w ∣^{2} - 2 u \cdot v + 2 u \cdot w - 2 v \cdot w . Substitute the known values: = 1^{2} + 2^{2} + 3^{2} - 2 (u \cdot v) + 2 (u \cdot v) - 2 (0) . = 1 + 4 + 9 = 14 . Therefore, ∣ u - v + w ∣ [c i t e_{s} t a r t] = 14 .

Try it yourself before checking the explanation above.

Let u, v, w be such that ∣ u ∣ = 1, ∣ v ∣ = 2, ∣ w ∣ = 3. If the projection v along u is equal to that of w along u and v, w are perpendicular to each other then ∣ u - v + w ∣ equals

2

7

14

14

Practice with timed mock tests and track your performance across Mathematics.