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.

The position vector `underset~a` of the group of hikers with respect to the starting point is

1. `underset~a = -5/2 underset~i - (5sqrt3)/2 underset~j`
2. `underset~a = -5/2 underset~i + (10 - (5sqrt3)/2)underset~j`
3. `underset~a = -5/2 underset~i + 10underset~j`
4. `underset~a = -(5sqrt3)/2 underset~i + 15/2 underset~j`
5. `underset~a = 5/2 underset~i + (10 + (5sqrt3)/2)underset~j`

Let point `M` have coordinates  `(a, 1,-2)`  and let point `N` have coordinates  `(-3, b,-1)`.

If the coordinates of the midpoint of  `bar(MN)`  are  `(-5, 3/2, c)`  and `a, b` and `c` are real constants, the the values of `a, b` and `c` are respectively

1. `−13, 2 and −1/2`
2. `−2, 1/2 and −3`
3. `−7, −2 and −3/2`
4. `−2, −1/2 and −3`
5. `−7, 2 and −3/2`

The distance between the points  `P(−2 ,4, 3)`  and  `Q(1, −2, 1)`  is

A.   `7`

B.   `sqrt 21`

C.   `sqrt 31`

D.   `11`

E.   `49`

The distance from the origin to the point  `P(7,−1,5sqrt2)`  is

1. `7sqrt2`
2. `10`
3. `6 + 5sqrt2`
4. `100`
5. `5sqrt6`