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Can unit vector have negative component?
Yes, a unit vector can have negative component since a unit vector has same magnitude and direction as a negative unit vector. Here is the general work out of the problem: Let |v| be the norm of (v1, v2). Then, the unit vector is (v1/|v|, v2/|v|). Determine the "modulus" or the norm |(v1/|v|, v2/|v|)| to get 1, which is the new norm. If we determine the norm of |(-v1/|v|, -v2/|v|)|, we still have the same norm 1.
Prove that Hilbert Space is a Metric Space?
The question doesn't make sense, or alternatively it is true by definition. A Hilbert Space is a complete inner product space - complete in the metric induced by the norm defined by the inner product over the space. In other words an inner product space is a vector space with an inner product defined on it. An inner product then defines a norm on the space, and every norm on a space induces a metric. A Hilbert Space is thus also a complete metric space, simply where the metric is induced by the inner product.
Applications of vector calculus in engineering?
Electromagnetic fields, gravitational fields and fluid flow. If you are an engineer you will come across vector calculus to handle three dimensional space.
What is null vector?
NULL VECTOR::::null vector is avector of zero magnitude and arbitrary direction the sum of a vector and its negative vector is a null vector...
What is a unit vector?
It is a vector whose magnitude is 1.It is a vector whose magnitude is 1.It is a vector whose magnitude is 1.It is a vector whose magnitude is 1.
