2. Show that the ry plane W = (r, y, 0) in R³ is generated by: (i)u = |2 and v= (ii)u = and v=

Q: 32. Find the equation of a plane through the origin and per- pendicular to x – y+ z = 5 and 2x + y–…

A: Note- According to Bartleby guidelines, we are supposed to do only one question. If you want more to…

Q: 3. Find the Scalar eguation of the plane containing the line rt) =<!,2,-37+ -3,2, 17 and the point…

A: Given problem:- Find the scalar equation plane containing the line  r (t)= &lt;1,2,-3 &gt; + t &lt;…

Q: 2. (3=(1,0,-4,3) Are the vectors u₁ = (0,1,2,-1), u₂ = (1,2,0,1), 42 = (1,0, -4,3) a linearly…

A: a) Are the vectors \( \mathbf{u}_1 = (0,1,2,-1) \), \( \mathbf{u}_2 = (1,2,0,1) \), \( \mathbf{u}_3…

Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: Let y = proj₁y = 3 -2 and u = -3 (a) Find the orthogonal projection of y onto u. 2 1 = (b) Compute…

A: Here we have to find orthogonal projection of y onto u and also we have to calculate distance d.

Q: If v = (1,2 ) draw all vectors w = (x, y) in the xy plane with v · w = x+ 2 y = 5. Why do those w's…

A:

Q: 2.b) Which vector is not normal at the plane defined by 2x - 4y-6z+1=0?

A: The solution is shown in step-2

Q: Find any two non collinear vectors on the plane x-y-3z +6=0

A:

Q: 6) Let U be the plane spanned by the two orthogonal vectors and in R. If v = (0), which one of the…

A: I think given options are incorrect.

Q: Let A(x,y,,z) and B(x,,y2; z,) be two known 3D points. The point M on the line AB divides the vector…

A: The vectors AB, AM and MB are collinear vectors. Therefore, consider the formula for the collinear…

Q: 5) Consider the vector function r = (9 – 2t, 4 + 2t, vZt²) a. Find the length of the path on 0<t<1.…

A: Given vector function The length of the path is found by the formula Given interval is 0 to 1

Q: 7. Let u = (2,1, −1) and v = (√√2, 1, 1). Find the decomposition of u into vectors that are parallel…

A:

Q: e. The plane through Po(2, 4, 5) perpendicular to the line x = 5+ t, y = 1 + 31, z = 4t

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: 3. Find the to Ihe bae coordinate vector of V relative (l,l, i), ( !!,0), when V= (a,b,c) こ

A: We suppose that (x,y,z) is the coordinate vector of  V relative to given basis so we can write V as…

Q: 15. Find in rectangular components the unit vector which is: (a) in the direction of E at P(2,3,-4)…

A: