Category: 0. BLOG

For φ = x²y + y²z + z²x, the directional derivative at (1,1,1) along u=(1,1,1)/√3 is A 10/√3 B 12/√3

For φ=x²y+yz², the gradient at (1,2,1) equals A A. (4,2,4) B B. (4,2,3) C C. (2,4,4) D D. (2,2,4) Explanation

For φ=xyz, the gradient at (1,2,3) equals A (6,2,3) B (3,6,2) C (2,3,6) D (6,3,2) Explanation ∇φ=(∂φ/∂x,∂φ/∂y,∂φ/∂z)=(yz,xz,xy). At (1,2,3) it

For φ(x,y,z)=x²+y²+z², the gradient at (1,1,1) is A (1,1,1) B (3,3,3) C (2,2,2) D (0,0,0) Explanation ∇φ=(2x,2y,2z). Substituting (1,1,1) gives

In vector calculus, the gradient of a scalar field gives what at a point? A Net flux B Circulation around

If |a|=|b|=1 and a·b=1/2, then |a−b| equals A 1 B √2 C 1/√2 D √3/2 Explanation |a−b|²=|a|²+|b|²−2a·b = 1+1−2(1/2)=1. So

If points A(2,1,0) and B(−1,3,4), vector AB is A (3,−2,−4) B (1,4,4) C (−3,2,4) D (−1,3,4) Explanation Vector AB =

For vector a = 3i−4j, magnitude |a| is A 1 B 7 C 5 D 25 Explanation Magnitude of a

In ai+bj+ck, coefficient a is A y-component B x-component C z-component D vector magnitude Explanation In component form a i

A vector has both A Magnitude and direction B Mass and weight C Length and breadth D Area and volume