Consider ℝ3 with the metric d((x1, x2, x3), (y1, y2, y3) = |x1 - y1| + |x2 - y2| + |x3 - y3|. i. Verify that d is really a metric. ii. State and prove the Bolzano-Weierstrass Theorem for ℝ3 with this metric.

Q: Let (l, m, n,), i = 1, 2, 3 be the direction cosines of 3 mutually perpendicular lines. Find the…

A:

Q: a) Find the vector that is parallel to the tanget to the circle x2 +y? = 100 at the point (3,4).

A:

Q: for 2. Given the vector space W given by W = Span Image A Image B Can you write W as a span of fewer…

A: Solution: We clearly see, image B can be formed by stacking two rows of two image A's each.  i.e.,…

Q: 7 Let C and D be points with position vectors c and d respectively. If |c| = 5, |d| = 7 and c. d =…

A:

Q: 4.) Correct of K vector representation for of terms B the velatie. positive normal and tangential…

A:

Q: Let* be the angle between the vectors ₁ and ₂. Let be the angle between the lines l₁ and ₂. We have…

A:

Q: Suppose u = (0, -5, -1) and v = (-2, 1, 4). Then: 1. The projection of u along v is -9/sqrt13 2. The…

A: Suppose we have  Then we have to answer the following...

Q: 2. If X(-2, -6, 5) and Y(3, -4, 1) are two points in R³ , determine: a) XY b) | XY | in reduced…

A:

Q: -15). Let y = a and the vector 2 = ba CM and let L- Span pan{[+]} [2] is Write y = y + z. where the…

A: Given that y=-51 and let L=span-11. We have to write the vector in the form y=y^+z, where y^=ab is…

Q: Verify that {u₁,u₂} is an orthogonal set, and then find the orthogonal projection of y onto…

A:

Q: Given is the plane V : a · x = 9 with a = (2, -3,6)t. Calculate the distance from O= (0,0,0) and…

A: Given that:The Plane  with To find: The distance from  and  to V.Concept:The distance d between a…

Q: let R = (1, 4, 3). RÓ has components (4, 1, 1), and Find the point Q such that v = sketch v.

A: Given: The components of vector v=RQ⇀ and  R= (1,4,3)  To find  Q and sketch v

Q: Let L₁ be the line passing through the point P₁(-3, 1, -2) with direction vector d=[0, -1, 2]T, and…

A: Expressing the equation of lines in vector form.

Q: The definition, u⚫v= = |u| |v| cos 0, implies the Cauchy-Schwarz inequality that |u•v|≤|u| |v|…

A:

Q: Prove that the di ("Manhattan") metric on R2 is really a metric.

A:

Q: Let S{v1,v2, V3}, where -1° 2. ; V1= -1 ; V1 = 1. 1. 1. 5. Show that S is a linearly dependent set,…

A:

Q: A free vector is Select one: O a. a directed line. O b. a directed line-segment in 3- space. c.…

A: A vector whose point of application is not fixed but magnitude and direction is, is called free…

Q: 7. Write the vector w in terms of u and v, given that the terminal point of w bisects the line…

A: This question is related to vectors, we will solve it using given information.

Q: 47. Determine if AP is tangent to circle 0. A A. yes B. no 5 12 13

A: Given.