Question

5) Let u and v be three-dimensional vectors and f(x, y, ) a scalar function. Which of the following expressions is not meaningful? A) (u-v) x Vf B) (u x v). Vf C) (u x v) of D) u · v + Vf| [6] Approximate Try? dy de using the midpoint rule with m= 1 and n = 2 (i.c. divide the region into two equal subregions by drawing a horizontal line segment). A) -64 B) 64 C) -80 D) 80

Answer 1

M given u and v be three dimensional vecton and f(Hry,2) be a scelean function then cleanly ur ès a scelan uxu is a verton If is a vecton hence Afl as a e un scelan urtlofl is the sum of to Scalen hence ID as meaning full since uxv is a vecton and If is a vecton hence (Uxv) x (ff) is a vecton hence c zs Meaning full, since uxv zs a veeta and If z's a vecta hence ruxv).(of) is a spalan hence B z's Meaning full Since uv is a colan and If zs a vecton - hence (M.v) x Hf) is the cross Product of scalan and vecton which is not meaning full hence A is not meaning full

I use the definition of dot and cross product and gradient to solve this problem