13. [Maximum mark 14) A plane is scheduled to fly from Las Vegas to Vancouver Vancouver is approximately 800 km west und 1400 km north of Las Vegas and has approximately the same altitude as Las Vegas. The plane takes off and ascends to a point that is 50 km due north of Las Vegas and 10 kuxn higher above sea level The plane then travels along a straight path that aiming for a point that is 50 km east of Vancouver with an altitude of 10 km. Throughout this question Las Vegas will be treated as the origin of a coordinate system (a) 1) Find a vector that is parallel to the direction of the straight path of the plane. [2] Hence, or otherwise, find a vector equation for the path of the plane. 12] The border between the USA and Canada runs directly East-West and is 30 km south of Vancouver (b) Find the position vector from Las Vegas to the point where the plane crosses the border 141 When the plane is 60 km from Vancouver it changes direction and aims directly for the city (e) ) Find the position of the plane when it changes direction 19 ii) Hence, find the total straight distance that the plane travels before changing direction. 12] 13. [Maximum mark 14) A plane is scheduled to fly from Las Vegas to Vancouver Vancouver is approximately 800 km west und 1400 km north of Las Vegas and has approximately the same altitude as Las Vegas. The plane takes off and ascends to a point that is 50 km due north of Las Vegas and 10 kuxn higher above sea level The plane then travels along a straight path that aiming for a point that is 50 km east of Vancouver with an altitude of 10 km. Throughout this question Las Vegas will be treated as the origin of a coordinate system (a) 1) Find a vector that is parallel to the direction of the straight path of the plane. [2] Hence, or otherwise, find a vector equation for the path of the plane. 12] The border between the USA and Canada runs directly East-West and is 30 km south of Vancouver (b) Find the position vector from Las Vegas to the point where the plane crosses the border 141 When the plane is 60 km from Vancouver it changes direction and aims directly for the city (e) ) Find the position of the plane when it changes direction 19 ii) Hence, find the total straight distance that the plane travels before changing direction. 12]