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The given question is related with vector space. We have to find a vector orthogonal to both 3 , 2 ,…

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Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.1: Vectors In Two Dimensions

Problem 36E

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In Problem,the vector v has initial point P and terminal point Q.Write v in the form that is,find its position vector. P =(1, 0); Q =(0, 1)
Assignment 4 Problem 6: Find a vector orthogonal to both ⟨2,2,0⟩ and to ⟨0,2,3⟩ of the form ⟨1,_____ ,_____ ⟩ correctly
If u = < 3 , 9 > and v = < -3, 1 >, find 1/3u - 2v. (this is a vector problem)
In Problem,the vector v has initial point P and terminal point Q.Write v in the form ai+bj+ck that is,find its position vector. P =(-2.-1,4); Q =(6,-2, 4).
In Problem ,use the vectors in the figure at the right to graph each of the following vectors. 3v + u - 2w
Questions (a) and (b) in this problem refer to the vectors u = 1 −2 2 and y = −2 1 −1(a) Find the orthogonal projection of y onto the line through u.(b) Write y as the sum of two vectors, where the first is in Span{u} and the second is orthogonalto u.
- It is a vectors problem - Simple solutions would be better, not too advanced Question: For what values of k will the line (x,y,z) = (k,-4,-6) + t(3,2,1) intersect the plane x - 4y +5z + 5 = 0 a) in a single point? b) in an infinite number of points? c) in no points?
5. Find the angle between the vectors (approximate to the nearest degree): u = [0, 1, 1] and v = [1, 2, 3]
Assignment 4 Problem 8: Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-4, 4, 1), Q = (-1, 7, 4), and R = (-1, 7, 9). (______,_____ ,_____ )
How would I solve this problem? Find the coordinates of a point P on the line and a vector v parallel to the line. (x-9)/4 = (y+3)/3 = z + 8 (image attached)
write the general solution to x+y+z+w=1 x+y-z-w=1 as a vector in the form of y or w I've tried this so many times and can't get it right, please explain how you got it.
I reached this same conclusion " Tx=Ax1x2⇒Tx=0110x1x2⇒Tx=x2x1" but had difficulty explaining it in words because it is only a reflection with respect to the y=x line if there is a negative value in either the x or y original vector. eg. (-3,2) => (2,-3) reflects across the x and y axis however if both values of x,y are negative of positive the values stay in the same quadrant and the reflection occurs over a corresponding diagonal midline. As far as I can tell, the values are transpose vectors of one another, but transpose is not a linear transformation. I know I must be confusing some theorem or missing something, but I cannot find it. Is there something I am misinterpretting? Sometimes online classes are extra difficult when asking for clarification isn't immediate or easy, so sorry for the needed follow up.

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(1, Find a vector orthogonal to both (3, 2, 0) and to (0, 2, -1) of the form