Find a vector equation of the line through the points \(A(-3,1,5)\) and \(B(0,2,3)\). (2 marks)
Vectors, EXT2 V1 EQ-Bank 8
Classify the triangle formed by joining the points `A(3,1,0), B(-2,4,3)` and `C(3,3,-2)`. (4 marks)
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Vectors, EXT2 V1 2021 HSC 3 MC
Which of the following is a vector equation of the line joining the points `A (4, 2, 5)` and `B (–2, 2, 1)`?
- `underset~r = ((4), (2), (5)) + λ ((1),(2),(3))`
- `underset~r = ((4), (2), (5)) + λ ((3),(0),(2))`
- `underset~r = ((1), (2), (3)) + λ ((4),(2),(5))`
- `underset~r = ((3), (0), (2)) + λ ((4),(2),(5))`
Vectors, EXT2 V1 SM-Bank 21
- Find the equation of the vector line `underset~v` that passes through `Atext{(5, 2, 3)}` and `B(7, 6, 1)`. (1 mark)
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- A sphere has centre `underset~c` at `text{(2, 3, 5)}` and a radius of `5sqrt2` units.
Find the points where the vector line `underset~v` meets the sphere. (3 marks)
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Vectors, EXT2 V1 SM-Bank 2
- Find values of `a`, `b`, `c` and `d` such that `underset~v = ((a),(b)) + 2((c),(d))` is a vector equation of a line that passes through `((3),(1))` and `((−3),(−3))`. (2 marks)
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- Determine whether `underset~u = ((4),(6)) + lambda((−2),(3))` is perpendicular to `underset~v`. (1 mark)
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- Express `underset~u` in Cartessian form. (1 mark)
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Vectors, EXT2 V1 SM-Bank 9
- Find the equation of line vector `underset ~r`, given it passes through `(1, 3, –2)` and `(2, –1, 2)`. (2 marks)
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- Determine if `underset ~r` passes through `(4, –9, 10)`. (1 mark)
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