Answered: Problem 5. (a) Prove that the vectors… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 14E

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Problem 5. (a) Prove that the vectors
V₁ =
V2 =
and v3 =
form an orthogonal basis of R³ with the usual dot product.
(b) Use orthogonality to write the vector v = (1,2,3) as a linear combination of V1, V2, V3.
(c) Construct an orthonormal basis from the given vectors.
(d) Write vas a linear combination of the vectors in the orthonormal basis you found in (c).

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Find a basis for R2 that includes the vector (2,2).
Calculate r' (t) and T(t) and evaluate T(1). r(t) = (6 + 7t,1², 5 – t²) (Give your answers using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) r'(t) = (7,2t,–2t) 7 -2t T(t) = V49 + 8? V49 + 8? Va9 + 8? Incorrect
Consider the basis B of R² consisting of vectors (-1, 2) and (-6, -3). Find x in R² whose coordinate vector relative to the basis B is [X]B=(4, 5). (Write your answer in the form (a, b) where a and b are real numbers.)
Either find the coordinates of the vector relative to basis B, or find the original vector from the coordinates relative to basis B. (a) v = (3,5,10); B = {(1,0,−1), (2, 1, −1), (-2, 1,4)} for R³. (b) v = (13,54); B = {(1,0), (0, 1)} for R². (c) [v]B = (10,-1, 4); B = {(1,0,−1), (2, 1, −1), (−2, 1,4)} for R³.
Let a = (5, 6, −4) and b = (-3, 4, −7) be vectors. (A) Find the scalar projection of b onto a. Scalar Projection: (B) Decompose the vector b into a component parallel to a and a component orthogonal to a. Parallel component: ( Orthogonal Component: ( " " "
Two soccer players are practicing for an upcoming game. One of them runs 10m from point A to point B. She then turns left at 90 degrees and runs 10m until she reaches point C. Then she kicks the ball with a speed of 10 m/s at an upward angle of 30 degrees to her teammate, who is located at point A. Write the initial velocity vector of the ball in component form, explicitly describing the basis vectors you are using.
How do I solve this in steps? Thanks
Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).
Determine nonzero vectors that are orthogonal to the following vectors. (a) (1, 5) (b) (6, −1) (c) (−4, −1) (d) (−5, 0)
Consider two vectors:

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