R lies between J and W on JW. Given that JR: RW = 3:4, R = (-5,1), and W = (6,8), find the coordinates of J.

Q: 5) Find the angle between the lines. y+2 %3D z-5 2x – 3 = y + 9 = 2z + 7 & x +1 = | 2 2.

A: Putting the value of drs of line , we can get angle

Q: The vectors a and b are such so that a = √10, b = 10 Find the value of lax bl. and a b = 30

A:

Q: Given d₁ = [2 11³ and A = [21]. find a vector d₂ = [3 a] that is conjugate with L2 respect to d₁.

A:

Q: Which of the following has coordinates ()? А. 27л/6 В. 29п/6 C.317/6 D.33t/6

A: To find the angle for which has the coordinates -32, 12.

Q: 4. Evaluate S. (z - 4) dz, where r is a contour from the two line segments, the first from z = -3 to…

A: The given question is related with complex integration. We have to evaluate the integral,…

Q: Q3. Evaluate [(A +B). (à – B)] if à = 2î – 3ĵ + 5k and B = 3î + j – 2k

A: Topic:- algebra  Note:- as per our guideline if more than one question uploaded than only one…

Q: 2. Demonstrate the following relationship involving the dot product and cross product (a) u. (v xw)…

A:

Q: Classify the following diferential equations. Write the order, linearity and the homogeneity of the…

A: Sol:- (a) y'''+ex y'' = x3+5xy2 order :- 3 :- as Highest order of differential equation is 3…

Q: 2. Demonstrate the following relationship involving the dot product and cross product (a) u. (V x W)…

A: a) To prove .c) To prove .Concepts Used:Commutativity for Multiplication: Commutativity for…

Q: If an ant is moving around a few food particles of different shapes scattered on the floor, in the…

A:

Q: 4. Evaluate S. (z – 4) dz, where r is a contour from the two line segments, the first from z = -3 to…

A: Contour integrals or line integrals along a path C   can be written as ∫Cf(z) dz=∫abf(z(t) z'(t) dt…

Q: 1. Let u = PQ and v = PR, where P = (2, –1,3), Q = (0,5, 1), and R = (5,5, %3D (a) u v (b) The angle…

A:

Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: Find the inverse of ƒ(x) = -x + b (b constant). What angle does the line y = -x + b make with the…

A:

Q: Q1 : Find the angle between u = 2i + j- 2k and v = i+j+k.

A: The angle between two vectors: - Consider two vectors a and b that are separated by an angle. Then,…

Q: Given the points C(-4, –5) and D(-1, 1), express the vector CD in terms of i and j.

A:

Q: Let à x b = -38 i +6 j 20 k Where a = -2 i + 4 j + 5 k and b = mi + 6 j − 2 k, ɓ Calculate m, là b,…

A: Basic formulas from vectors will be used.

Q: i = [4,24, 46] = r·õ+B so that i = [-4, 1,7] and B is perpendicular to

A: Introduction: The dot product of two vectors lies in the same plane as the two vectors. if two…

Q: 1. Consider the lines x = -1+ 2s 3 – z l1 : 2 and l2 : y= s 4 -2 z = 5+ s а. Find two unit vectors…

A: This is a question of vector Algebra.

Q: Find the length and direction (when defined) of u x v. When : u = 2i +2j -k; v = -i + k;

A:

Q: Determine C if u=v=0 (20 — 5и + 3)dv — (20 + 4и — 6)du 3 0 - 3 27 -1

A: Let's find.

Q: Let a(t) = (– 5, 5, – 2)t + (2, 4, 6) and b(u) 3 (- 3,0, - 4)и + ( - 2, — 8, — 5). Find the acute…

A:

Q: Q: Find the angle between the lines whose direction cosines satisfy the equations 1+m +n =0,12 + m²…

A:

Q: E Find the angle between u = 2i-j+2k and vzi-zj +2k Sol.

A:

Q: Given u= -i + j and v= i+9j, find the dot product u v.

A: To find the dot product rule is that, just multiply the corresponding coefficients of i and j and…