In a regular hexagon ABCDEF point G is the midpoint of line segment EF, point S the intersection of lines AC and BG, and |AS| : |SC| = 3:4. The side of the hexagon ha length 2. Denote = BA and b = BC. and (a) Write the vector SG as a linear combination of vectors (b) Compute the length of the vector AC. (c) Compute the angle between vectors AC and AF.

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 6j as…

A:

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 4j as…

A:

Q: Given vectors: A(6.4,3), B(0.4.6) and C(8.2.1) forms a triangle. Find the angle at point B

A: Solution

Q: Given vectors a=-37-9)andy=-12t-13, find vector x

A: We need to obtain the difference of the two vectors.

Q: Given u = , v = -5i - j, and w (AB) is defined by the points (1, 6) and (-2, 8). a Find v in…

A: This is  a problem of vector. By dissolving vector in x and y parts we will convert it into…

Q: Find a unit vector that has the same direction as 8i - j+ 4k. Write the numerical coetficient in…

A:

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as…

A:

Q: Given the points P(-2, 6, -2), Q(5, 7, 2) and R(3, 4, −1). Find the angle, 0, in degrees, that is…

A:

Q: Solve the problem. Find the area of the triangle determined by the points P(-3, 6, -4), Q( 2, 10,…

A:

Q: Simplify each vector operation. a) j·(-j) b) (i ×j)·k c) (i ×j)xk

A:

Q: 4 In the following, b = a = c = Calculate: a atb b c-b c 2a +b d 3c- 2b

A:

Q: Given vectors a = and b = , find 3a - 2b.

A:

Q: Let A, B, C and D be consecutive points of a parallelogram. Point E divides the diagonal AC so that…

A: Given A, B, C and D be consecutive points of a parallelogram. Point E divides the diagonal AC so…

Q: The three vertices of a triangle are at A (7,-1,3), B (-3,3,-4) and C(-3,1, 5). Find: (use Dot…

A:

Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symme…

A: