3) Consider stress of a body at a particular point is give in the form of Q(x1, x2, X3) = xỉ – x – 4x1x2 + 4x2x3. Find an orthogonal change of variable that eliminates the cross product terms in ) Q(x1,x2, X3).

Q: Which of the points P = (-1,4,-7) and Q = (6,-1,5) is closest to the z-axis? OQ (6,-1,5) OQ (6,-1,0)…

A:

Q: Find the Cross product of A= and B=

A:

Q: Find the cross product x where = 71-7j -4k and 7 = (-4,-3, 4). úxv=

A:

Q: Find an equation of the line through (-2, 5, 3) that is perpendicular to both u = (1, 1, 2) and the…

A:

Q: Use the definition to determine whether or not =(3,5,-2)'. =(-2,1,4)', and =(1,3,7) are linearly…

A: We have to check whether given set of vector is linearly independent or dependent.

Q: The distance from (-3,-4,-7) to the xz-plane is (A) -4 (B) (C) -3 (D) 3 (E) 4.

A:

Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

A:

Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

A:

Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

A:

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

A:

Q: Find the gradient of w= 3x² - 5y* + 2z at the point (1, 1, -2)

A: The given function is: w=3x2-5y2+2z2

Q: Given u, v and w from question 3, find (a) the angle between u and w,

A: u = (4,0,-2) and w = (2,1,6)

Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: x is cross product

A: Given, let f,g:R→R3 be differentiable functions. The derivative of their vector cross product is…

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)