If X, Y, Z ER and x≤Z, show that XL Y S z if and only if |x-y| + | y-z| = |x-z). Interpret geometrically.

Q: Consider the points A(2, a,0), B(0,1,B),C(1,1,B) where aand Bare negative real numbers. Find a and…

A: To add or subtract, two or more vectors add or subtract the corresponding components of each vector.

Q: let à = (3,4,5) and To (5,2, 6) a Find (2-6) x (a+b)

A: We need to find out the cross product.

Q: let a1 is (-3,2,6) a2 is (-9,-7,-2) and b is (-18,-27,-23). Is b in the span of of a1 and a2

A: The objective of this question is to determine whether the vector b is in the span of vectors a1 and…

Q: {(r.0):3<rs4 and so<- Neatly sketch the set of points

A:

Q: Let u= and v= identify 3u+v???

A: We have to identify 3u+v for the given vectors: u=2, -3 and v=4, -1. Finding 3u: 32, -3=6, -3

Q: TRUE or FALSE: A\B = A when A and B are disjoint

A: Given statement ,A|B=A then A and B are disjoint

Q: Let ū = (3, – 4, – 10) and i = (– 7, – 2, 0). - 2ü + 20 (-8,-12 - 20)

A: Given :-  u=&lt;3,-4,-10&gt;  v=&lt;-7,-2,0&gt;  To find:-  2u+2v

Q: 2. secx d X secx

A: ∫sec2x5-sec2xdxPrepare for substitution, use:sec2x=tan2x+1

Q: 3) Let x = (-1,3,2,-4), and y = (1,0,2,3). Find the following distances || x = || = ? []x - || =?

A:

Q: Let u = and v = Find each quantity: a) (u)(v)  b) (u)(u)  c) (v)(v)

A: Given: u =&lt;4,-3&gt; and v =&lt;-2,7&gt;