multivariable calculus, vectors calculus 1. Indicate whether the following statements are true or false. No justification necessary.(a)vector (gx, Jy, -1) at P is orthogonal to a level surface for G(x,y, z) := g(x, y) + z.If g(x, y) is a 2-variable function and P is a point on the graph of g, then the 3-dimTRUEFALSE(b)vector (gr, 9y, –1) at P is orthogonal to a level surface for G(x, Y, z) := g(x, y) – z.If g(x, y) is a 2-variable function and P is a point on the graph of g, then the 3-dimTRUEFALSEif two lines in R³ do not intersect, then they must be parallel.TRUEFALSE(d)function f, and furthermore f(Q) > f(P), then the person must have been walking in thedirection of the gradient Vf throughout their walk.If a person walks from point P to point Q in the domain of some differentiableTRUEFALSE(e)function f, and furthermore their path was pointing in the direction of Vƒ throughouttheir walk, then we must have f(Q) > f(P).If a person walks from point P to point Q in the domain of some differentiableTRUEFALSE(f)function f(x, y) (viewed on the entire xy-plane without constraints). Suppose further thatP happens to lie on a constraint curve g(x, y) = 0. Then P must also give an absolutemax for f subject to the constraint g = 0.Suppose we have found that the point P gives an absolute max for the continuousTRUEFALSE(g)function f(x, y) subject to the constraint g(x, y) = 0. Then Q must also give an absolutemax for f viewed on the entire xy-plane without constraints.Suppose we have found that the point Q gives an absolute max for the continuousTRUEFALSE

As per the bartleby policy, I will be solving first three options. For other's please post it again.

1. Indicate whether the following statements are true or false. No justification necessary. If g(x, y) is a 2-variable function and P is a point on the graph of g, then the 3-dim (a) vector (ga, Iy, –1) at P is orthogonal to a level surface for G(x, Y, z) := g(x, y) + z. TRUE FALSE If g(x, y) is a 2-variable function and P is a point on the graph of g, then the 3-dim (b) vector (g2, Iy, –1) at P is orthogonal to a level surface for G(x,y, z) := g(x, y) - - 2. TRUE FALSE (c) if two lines in R³ do not intersect, then they must be parallel. TRUE FALSE