The dot product of two vectors can be written in the form x = 00 s+ X1 X2 and y = in R" is defined by * · Ý = X1Y1 + X2Y2 + ... + xnYn. The vectors and are called perpendicular if · y = 0. Any vector in R³ perpendicular to Y1 Y2 or N ∞o

Q: a line is parallel to the vector i+ 5j+3k and passes through the point P = (6, 2, 4), then the…

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Q: Consider an inner product on two P₂ vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(2)g(2): 1) (−4 +…

A: The inner product on two P2 vectors as f,g=f-1g-1+f0g0+f2g2

Q: Please justify whether these statements are true of false. a. If u and v are vectors in R^3, then…

A: Objects with both magnitude and direction are called vectors. The vector's size is determined by the…

Q: a. A nonzero vector perpendicular to both [-1. 3, 4] and [-2. -1, 3].  b. The distance from (2, -1,…

A: Let's go through each of the questions:a. To find a nonzero vector perpendicular to both [−1,3,4]…

Q: Suppose that u₁ and u2 are vectors with ||u₁|| = 2 and ||u2|| = 3. You are also given that u₁ · U₂ =…

A: Given that  and  are vectors such that .Given that  and  for .We need to find  for .We need to…