3] By using the properties of dot and cross product, prove the following: a) (ü x 7). v = 0. b) (w – i) x (w + 7) = 2(w x v). %3D c) W x (V x Ũ) = (w.Ū)V – (W.V)Ū. -

Q: Consider the points A(2, a,0), B(0,1,B),C(1,1,B) where aand Bare negative real numbers. Find a and…

A: To add or subtract, two or more vectors add or subtract the corresponding components of each vector.

Q: p) Classify the following models as ARIMA(p,d,q). i) (1-B)x, = (1-0.3B),. ii) (1-0.5B+0.25B²)Vx, =…

A: ARIMA means auto regressive integrated moving average, It ia also written in the forn ARIMA(p,d,q)

Q: Find the cross product u x v where i = 3i +6j +9k and v = (- 2, – 4, 5). ux v =

A:

Q: (x- 2y) dA on the parallelogram P bounded by y = 5 – 2x, y = 7- 2x, y = 3x – 6, and y = 3x + 2. Use…

A:

Q: Find the cross product i x v where i = 2i +2j -3k and i = (- 8, – 6, 3). i x ở =

A:

Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

A:

Q: 13. Let A be the set A = {a, b, c, d}. Consider the relation R on A given by R = {(a, a), (b, b),…

A:

Q: How, Form P.D.E. from: a (3) Ucx,y) = (x²+a)lytb)

A:

Q: x y ● = Find the dot product of 1 18 0 — -2 and y = 1 2 4 ●

A:

Q: What is v(v × w)?

A: we need to find the value of

Q: Determine values of x and y so that v · w = 0 and v · u =

A: There are vector representation given as, v=x1y , w=x-20  and u=0-9y. To find the value of  x  and y…

Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

A:

Q: 7. (50 u) du + (3v - 7u) dv 0. ANS. (3v +u) = c(v u).

A:

Q: 2. Evaluate (3xy+iy²)dz along the straight line joining z = i and z = 2 – i.

A: Given the Integral, ∫i2-i(3xy+iy2)dz We, know that z=x+iy ⇒dz=dx+idy, When z=i    ⇒x=0 and y=1  When…

Q: Find the area of the triangle formed by the points A = (3, –1, 2), B = (1, 1, 0), and C = (1,2,–1).

A:

Q: Let v = (5, 8) and w = (4, 5). What is the dot product v · w?

A:

Q: Find the cross product u x 7 where u úxv- 71 +5j +k and 7 (5,- 4,7).

A: This question can be solved using the concept of cross product of vectors.

Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the area of the triangle UVW

A: