4) If u = 3y e, - xe, +5e,, v xe, +(y-z)e, and a = 5x - y+ yz Calculate a) u.v b) u X v c) VX v d) Va e) Va f) V.u

Q: Sara draws the 4 of hearts from a standard deck of 52 cards. Without replacing the first card, she…

A: Given, Sara draws the 4 of hearts from a standard deck of 52 cards without replacing. a) we know…

Q: 9. Given that u = (1,5) and v = (-2,3), determine the following %3D -3u – 4v =

A:

Q: Let u = (3, 2, x) and v = (2x, 4, x). (a) Find all possible values of x that make u and v…

A: Given thata)We have to find all possible values of x that make u and v orthogonal.b)We have to find…

Q: Consider the vectors u=(2,3,-5), V = (-3, -2,6) and w=(-4,8,4). Calculate u.v

A: We have to find u.v

Q: 10. Find a unit vector in the same direction as PQ if P = (5, 4) and Q (3, 7). %3D

A: The solution is given as

Q: if u = (-1,0) and v = (3,-1), then 2u - 3v is:   a)   (-10, -3)   b)  (-10, 3)   c)  (10, -3)…

A:

Q: 4. Given vectors: =(4,9), v = (-8, 15) and w=(2, 10) a) Show that and w can span R².

A:

Q: 1: Let u = (-3,2, 4) and v = (2, -4,6). a) Find u o (v), b) Find u x v. c) Find Proj,u.

A: Here given that                        u=(-3, 2, 4)                and  v=(2, -4, 6)

Q: Find u ∙ (v × w)   if u = ⟨1, 1, 1⟩ , v = ⟨2, 1, 0⟩, w = ⟨0, 0, 1⟩

A: Given: u=1,1,1, v=2,1,0, w=0,0,1 we know that scaler triple product S.T.P. of given three vectors…

Q: 9. Let A=span{v = (-1,–1,2), i = Projau. (2,3,0)} and w (1,2, 3). Find

A:

Q: The point of intersection of y = x² + 6 and x = 2 is ... A) (1,8) B) (2,8) C) (2, 10) D) (10, 2)

A:

Q: 13. 2 [3] and u = [4] vectors, one in Span {u} and one orthogonal to u. Let y = . Write y as the sum…

A:

Q: Compute u X v.

A: Here given vector as u=3-12, v=011 These vectors can be written as u=3i-j+2kv=j+k

Q: post office sells 4-cent sheep stamps and 2-cent sunset stamps. Cole bought 5 stamps spent exactly…

A:

Q: 5. Suppose that a, b and care vectors such that |a| = 2, |6| = 1, || = 5, a·b = 0, a. c = 3 and b c…

A:

Q: and u = Find the component of y orthogonal to u. Let y

A:

Q: Let u = and v = . Now, w = is a linear combination of i and v. That is, w = aju + azv. Determine…

A: Answer:

Q: two bees leaving an area in a straight path. Bee's 1 path: r1(t) = + t and Bee's 2 path: r2(s) =…

A:

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: 25. Determine the x- and y-intercepts. a) [x, y] = [2, –4] + t[3, –1] b) [x, y] = [-8, 11] + t[5, 2]…

A: The given equations are in parametric form. To find x-intercept put y=0 and get the value of…

Q: 10. Let ā = (1,2) and b= (2,1). Find projz(ā). Then show that ā– projz(ā) is orthogonal to b…

A:

Q: 21. Given vectors u = (1,3) and v = (-6,2). a) Find u - 3v b) Find Ju + v].

A:

Q: 50° S. 80° R 60° 100 7. 7.

A: The measure of the arc length is double than the angle formed by that arc to the circumference of…

Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: Que. 1: Examine the following vectors for linear dependence X, =[1 2 4], X, = [2 -1 3], X, =[0 _1…

A: Write these vectors as rows in the matrix, convert the matrix to echelon form. If the echelon form…

Q: Let u= (1, 1, 4, 5), v = (1,4, -4,9) and w = (3, 1, 2, 3). Evaluate: a) dx2 dx3dx4(u, v, w) = b)…

A: Step 1: Step 2:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.