Vector Calculus - U24MA152

When two vectors in the same direction are added, the magnitude of resulting vector is equal to _______

• Sum of magnitudes of the vectors

• Difference of magnitudes of the vectors

• Product of magnitudes of the vectors

• Sum of the roots of magnitudes of the vectors

Calculating the relative velocity is an example of ______

• Vector addition

• Vector subtraction

• Vector multiplication

• Vector division

The Gradient of a constant is a null vector.

• True

• False

The temperature at a point (x,y,z) in space is given by T(x,y,z) = x^2 + y^2 - z. A mosquito located at (1,1,2) desires to fly in such a direction that it gets cooled faster. Which of the following direction it should fly?

• 2i→ + 2j→ - k→

• 2i→ - 2j→ - k→

• 2i→ + 2j→ + k→

• 2i→ - 2j→ + k→

If A and B are irrotational vectors, than Axb is -----

• irrotational

• gradiant

• Solenoidal

• None of these

Gradient of a scalar function is a_________ and the divergence of a constant is______

• vector and zero

• scalar and zero

• scalar and vector

• None of these

Divergence of a vector is a ---------- and curl of a vector is a ---------

• Scalar, vector

• Vector, Scalar

• Vector, Vector

• Scalar, Scalar

The Gauss divergence theorem converts

• line to surface integral

• line to volume integral

• surface to line integral

• surface to volume integral

The Green's theorem is related to ------ theorems mathematically.

• Gauss divergence

• Stoke's

• Euler's

• Leibnitz's

The Green's theorem relates -----

• line & surface integral

• line & volume integral

• surface & volume integral

• None of these