Select all possible vector equations for the line through the points (1,1,1) and (3,4,5). OF (t) = (1, 1, 1) + t(3,4, 5) O 4) T (t) = (3,4, 5) +t(2,3, OF (t) = (1,1, 1) – t(4, 6, 8) OF(t) = (5, 7, 9) +t(2,3, 4)

Q: 13. Find a vector equation of the line through (2, 1) parallel to (x, y) = (-2,7)+t(3,5). 14. Find a…

A:

Q: Determine (x, y, z) for each figure. Then find the component form of the vector from the point on…

A:

Q: 6. Determine if the vectors vị = (1, -1,3, –1), v2 = (1, –1, 4, 2), v3 = (1, -1,5, 7) dependent or…

A: We have to find that given vectors are linearly dependent  or linearly independent.

Q: Use the function to find the image of v and the preimage of w. T(v1, v2, v3) = (4v2 - v1, 4v1 +…

A:

Q: 5 Decide the dependence or independence of (a) the vectors (1, 3, 2) and (2, 1, 3) and (3,2,1) (b)…

A: The objective of this question is to determine whether the given sets of vectors are dependent or…

Q: 1. O (x, y, z) = (1,2,3) + t(4,5,1) 2. O (x, y, z) = (1,2, -3) + t(4, -5,1) 3. O (x, y, z) = (4,5,1)…

A: Explanation of the solution is given below...

Q: Find a vector equation for the line through the point (4, 5, -1) perpendicular to the vectors , 6,…

A: we have to find the line equation passing through point (4,5,-1) and perpendicular to the vectors…

Q: Use the function to find the image of v and the preimage of w. T(Vy. V2) = ( V2, 2v1 - v2), v = (7,…

A:

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 - V1, 4V1 +…

A:

Q: { (1, 2, 1), (2, 1, 5) , (1, –4, 7) } (i) Prove that is linear dependent subset of R³. (ii)…

A: A set is linearly dependent if and only if one vector is linear combination of other vectors.

Q: Which vector equation below represents the line in R³ that passes through the point (-4, 5, 7) and…

A:

Q: 5 Decide the dependence or independence of (a) the vectors (1, 3, 2) and (2, 1, 3) and (3, 2, 1) (b)…

A: The objective of this question is to determine whether the given sets of vectors are dependent or…

Q: Use the function to find the image of v and the preimage of w. T(V,, V2, V3) = (4v, - v,, 4v, +…

A:

Q: (i) Prove that { (1, 2, 1) , (2, 1, 5) , (1, –4, 7) } is linear dependent subset of R³. (ii)…

A:

Q: Find the vector in component form with initial poi

A:

Q: Find the B-coordinate vector for p(t)=4+3t-2t²-5t³ B={1-2t²_t³,t +3t³,1 +2t+t²} a. (2,-1,2) b.…

A:

Q: Which of the following is a direction vector for the line through А (3, — 2) and В (1, 2)? Select…

A:

Q: Use the function to find the image of v and the preimage of w. T(V, V2, V3) = (4v, - V, 4v, + 5v2),…

A:

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4v, +…

A:

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Draw the vectors in standard position in R2 with their tails at the point (2, -3).

A:

Q: Consider the vectors v₁ ví = (1,2,3,0), v = (0,1,2,3) and vg = (2,3, 4, -3) Let (1, 1, 1, 1) w (a)…

A: