4. Prove that the vectors a= (1,1,1); b-(1,-1,0) and e-(-1,-1.2) are orthogonal to each other! 5. Determine the size of angle ABC if the vertices are A(1,2,3), B = (-4,5,6) and C = (1,0,1)!

Q: 1. y -2+ 2.

A:

Q: 2.) Wrile pach vector below of the vectors in s.Cif possible), 0s a linear combination 5=d…

A:

Q: 4. Given 3 points: A(2, 1, 1), B(2, 2, 2), and C(4, 2, 2), compute the normal vector for the…

A:

Q: Which of the following pairs of vectors are perpendicular to each other? a) (4, 14, -18) and (6, 21,…

A:

Q: Which ONE vector is parallel to (4, 9, 16)? (a) (20, 0, 8) (b) (6, 27/2, 24) (c) (1/4, 1/9, 1/16)…

A: We will find which option is correct.

Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

Q: Consider the vectors u=(2,3,-5), V = (-3, -2,6) and w=(-4,8,4). Calculate u.v

A: We have to find u.v

Q: 2) (i) Find the direction cosines for v= he sum of their squares equals 1. (2,3,4). (ii) Verify that

A: Direction cosine and ratios

Q: 4. Given vectors: =(4,9), v = (-8, 15) and w=(2, 10) a) Show that and w can span R².

A:

Q: 7. Given three point A(1, 1, 3), B(-14, 4, 21) and C(-4, 2, 9), a) use a vector method to show that…

A: We have to solve given Questions.

Q: 5. Let A = (4,3), B = (0, 1), and C = (−3, 7). (a) Find the vectors AB, BC, and AT. (b) Prove that…

A: Step 1:It is provided that, A=(4,3),B=(0,1), and C=(−3,7). (a) Then, it is obtained:AB=B−A…

Q: 11. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors…

A:

Q: 22. Given that the vectors a = 3i-4j-4k, b = 2i-j + 3k, and c = 4i-3j +5k. The %3D %3D projection…

A: Here let d= a+b d= a + b⇒d = 5 i -5j -kProjection length of vector d = (a+b) on c is given by |d|…

Q: 12. Given a point P(1,-2,-4) and a point P2(3,1,-5), find a unit vector that has the opposite…

A: Step 1:Step 2: Step 3: Step 4:  thanks...