Find vector equations for the lines

Assignment Help Mathematics

Reference no: EM131214237

Vectors

Assessment

1. ABCDEF is a regular hexagon in which BC^→ represents b_ and FC^→ represents 2a_.

Express the vectors AB^→, CD^→ and BE^→ in terms of a and b.

2. If the position vector of A is 2i + 3j and the position vector of the point B is 3i - 5j, find:

(a) |AB^→|,

(b) the position vector of the midpoint of AB.

3. Find vector equations for the following lines:
(a) A = (2, 5, 9), m = 2i -5j + k
(b) A = (1, 6, 2), B = (3, 4, 3)

4. Convert the vector equations from the previous question into their parametric and cartesian forms.

5. Find the angle between the vectors a_ and b_ if

(a) a_ = i + j + k + λ(2i - 4j + 5k),
b_ = 2i + k + μ(i + 3j + 8k)
(b) a_ = 3i - j + λ(2i - 3j + 6k),
b_ = j - k + μ(i + j)

6. State whether the following pairs of lines are parallel. If they are not parallel determine, where possible, the point of intersection.

(a) r_ = i + j - k + λ( 2i - 3j + k)

r_ = 3i - 2j + 5k + μ( i + j - k)

(b) r_ = i + 2j + k + λ( i - j + 3k)

r_ = 2i - k + μ( 2i - j + 11k)

x/2 = (y + 5)/3 = (z-3)/4

Reference no: EM131214237

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