PYQs Based Test - 08 : Vector Identities and Properties

For a vector field $\vec{A}$, which one of the following is FALSE?

A triangle defined by A(2, -5, 1), B(0, 2, 4) and C(0, 3, 1). What is area of the triangle?

The divergence of the vector field V = x² i + 2y³ j + z⁴ k at x = 1, y = 2, z = 3 is ________

Given the vector A = (cos x)(sin y)âₓ + (sin x)(cos y) â${}_y$, â${}_y$ denote unit vectors along x,y directions, respectively. The magnitude of the curl of 𝑨 is ______.

The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.