Math Problem 5024 :( Vectors

[ailg1996]

AOA everyone this question appeared in my Beaconhouse Mock Exam can some1 help me



Here it is
The Diagram shows a regular hexagon surrounded by six equilateral triangles. The vector PV = a PO = b
In terms of a and/or b . Write down an expression for
iR
ii:OV
iii:ZU

Diagram in attachment

 

[abcde]

Wa alikum asalaam!
I remember doing this one all right!
(i) PV = VW = WR (sides of identical equilateral triangles)
=> vector PR = 3a
(ii) OV = PV - PO = a - b.
(iii) ZU = 2a.
Did this help? I can explain if you want.

 

[abcde]

By the way, the syllabus code is 4024!

 

[Firebender]

lemme explain. A vector is a quantity of movement. It INCLUDES DIRECTION AND DISTANCE.

The sides of a regular hexagon are all equal. The question also says each triangle is equilateral(all sides are equal). If the base of each triangle is same then we can assume, the length is same as well. So we know that DISTANCE is equal everywhere.

But the vectors include distance AND DIRECTION. Any line moving the same amount in the same direction is automatically an equal vector. Are the 3 sides of the triangles between P and R equal? Than its just the vector " a " times 3.
1) 3a

in (ii) O is the starting point and V is the destination. Any combination of vectors that starts at O and ends at V = OV. Basically we're supposed to use the vectors 'a' and 'b' to make a path from O to V. Its like a puzzle.

solution: If you turn 'b' backwards it becomes '-b' and completes a STRAIGHT path(or the puzzle) going from O to V. That maakes the path '-b+a' which can also be written as 'a-b' like abcde did.

(iii) PV is the same vector as ZY or YU cuz they're the same direction and distance. so ZU = 2a.

 

[abcde]

Exactly!