Aussie Maths & Science Teachers: Save your time with SmarterEd
The sum of two unit vectors is a unit vector.
Determine the magnitude of the difference of the two vectors. (3 marks)
\(\text{Vectors can be drawn as two sides of an equilateral triangle.}\)
\(\text{Using the cosine rule for the difference between the two vectors:}\)
| \(c^2\) | \(=a^2+b^2-2ab\, \cos C\) | |
| \(=1+1-2\times -\dfrac{1}{2} \) | ||
| \(=3\) | ||
| \(c\) | \(=\sqrt{3}\) |
\(\abs{v_1-v_2} = \sqrt{3}\)
Let `underset~i` be a unit vector pointing east and let `underset~j` be a unit vector pointing north.
A group of hikers travels 5 km in the direction south 30° west and then north for 10 km before stopping for lunch at position vector `(a underset~i, b underset~j)`.
Find the values of `a` and `b`. (2 marks)
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`sin30 = x/5 \ => \ x = 5/2`
`cos30 = y/5 \ => \ y = (5sqrt3)/2`
`P_1\ text(vector:)\ (-5/2 underset~i, -(5sqrt3)/2 underset~j)`
`P_2\ text(vector:)\ (-5/2 underset~i, (10 – (5sqrt3)/2)underset~j)`
`:. a=-5/2, b=10 – (5sqrt3)/2`
The vectors `underset~a` and `underset~b` are shown.
Which diagram below shows the vector `underset~v = underset~a - underset~b`?
| A. |  |
| B. |  |
| C. |  |
| D. |  |
`=>D`
The projection of the vector `((6),(7))` onto the line `y = 2x` is `((4),(8))`.
The point `(6, 7)` is reflected in the line `y = 2x` to a point `A`.
What is the position vector of the point `A`?
`text(Graph the projection and reflection:)`
`=>B`
Maria starts at the origin and walks along all of the vector `2underset~i + 3underset~j`, then walks along all of the vector `3underset~i - 2underset~j` and finally along all of the vector `4underset~i - 3underset~j`.
How far from the origin is she?
The diagram shows a grid of equally spaced lines. The vector `overset(->)(OA) = underset~a` and the vector `overset(->)(OH) = underset~h`. The point `Q` is halfway between `F` and `H`.
Which expression represents the vector `overset(->)(EQ)`?
`overset(->)(EQ) = 1/2underset~h – 1/4underset~a`
`=> A`