My Year 11 Spesh Question Thread

[pinklemonade]

Hey guys I've been struggling with specialist this year and I would appreciate any help! :-)

I need help with the following question:

The angle between vectors a = 2i + 3j + 5k and b = -4i + mk is 90 degrees. The value of m is:

A) 3/8
B) 8/3
C) 8/5
D) 5/8
E) 5

[RKTR]

Hey guys I've been struggling with specialist this year and I would appreciate any help! :-)

I need help with the following question:

The angle between vectors a = 2i + 3j + 5k and b = -4i + mk is 90 degrees. The value of m is:

A) 3/8
B) 8/3
C) 8/5
D) 5/8
E) 5

When angle between vectors is 90 degrees, a.b=0

2(-4)+3(0)+5m =0
-8+5m=0
m=8/5

[pinklemonade]

When angle between vectors is 90 degrees, a.b=0

2(-4)+3(0)+5m =0
-8+5m=0
m=8/5

Thank you so much!
I can't +1 you right now since I am a new member, but I will be sure to when I can :-)

[pinklemonade]

The bicycle moves with a force described by vector . Wind resistance acts against the bike in the opposite direction of its movement. The wind resistance vector could be:

a)
b)
c)
d)
e)

-


A vector in the opposite direction of a=i+2j-k with magintude of 10 is:

a.) 10i+20j-10k
b.) -10i-20j+10k
c.)
d.)
e.)

[RKTR]

vector=10[i+ root(3) j]
to find vector of wind resistance which acts in opposite direction, add negative sign in front
-10[i+root(3)j]
however it doesnt say the magnitude is the same so the number in front does not have to be 10.
so it could be k[i+root(3)j] where k is any negative number
looking at the choices, the answer will be (a)


find unit vector first which will be 1/root(6) x [i+2j-k]
opposite direction so add a negative sign in front.
-1/root(6) [i+2j-k]
magnitude=10
so vector= -10/root(6) [i+2j-k] which also equals 10/root(6)[-i-2j+k] which is (e)

[pinklemonade]

Could someone please help me solve this, thank you!!

[RKTR]

Could someone please help me solve this, thank you!!

Draw a parallelogram. You will see that AD is parallel to BC.
Vector AD= vector BC
             BO+OC=BC
             BC=-OB+OC
                  =2i-j+k