Question

Given vectors u and v. Suppose that 2u · v and 2u ⨯ v are orthogonal, and ||v|| = 3. Find ||u||. Option 1: ||u|| = 1 Option 2: ||u|| = 2 Option 3: ||u|| = 3 Option 4: ||u|| = 6

Answer 1

To find the magnitude of vector u (||u||), we can use the given information and solve for ||u|| using the dot product and cross product properties of vectors. The correct option is none of the options provided.

Step-by-step explanation:

To find the magnitude of vector u (||u||), we can use the given information. Since 2u · v and 2u ⨯ v are orthogonal, their dot product must be zero. We can write this as (2u · v) ⋅ (2u ⨯ v) = 0. Expanding this equation, we get 4(u · v) ⋅ (u ⨯ v) = 0. Now, we know that the cross product of two vectors is orthogonal to both vectors. So, we have 4(u · v) ⋅ (u) = 0. Since the dot product of two vectors is zero when they are orthogonal, we can conclude that (u · u) = 0. Solving for ||u||, we get that ||u|| = √0 = 0. Therefore, none of the options provided in the question is correct.

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