A105 Vectors

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A105 Vectors

WB1 In the diagram opposite, find the following vectors in terms of a, b, c and da) P⃗S b) R⃗P c) P⃗T d) T⃗S

WB2 Any vector parallel to a may be written as λa, where λ (lamda) is a non-zero scalar (ie - represents a number…)Show that the vectors 6a + 8b and 9a + 12b are parallel…

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A105 Vectors WB3 In triangle OAB O⃗A=a , O⃗B=b , P divides OA in the ratio 3:2, and Q divides OB in

the ratio 3:2 a) Show that PQ is parallel to ABb) Given that AB is 10 cm in length, find the length of PQ

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A105 Vectors

WB4

WB5 In the diagram, PQ = 3a, QR = b, SR = 4a and PX = kPR. Find in terms of a, b and k:

a) P⃗S

b) P⃗X

c) S⃗Q

d) S⃗X

e) Use the fact that X lies on SQ to find the value of k

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P Q

RS

X

3a

4a

b

A105 Vectors

WB A6 OACB is a parallelogram. O⃗A=a O⃗B=b The points M, S, N and T divide OB, BC, Ca and Ao in the ratio 1:4 respectivelyThe lines ST and MN intersect at point D a) Express M⃗N=¿ in terms of a and bb) Express S⃗T=¿ in terms of a and bc) Show that the lines MN and ST bisect one another

WB A7 Given that: 5a−4 b=s (2a+b )+ t (a−b ) find the value of the scalars s and t

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D

A105 Vectors

WB8 Given that a=2 i+12 j, b=12i−11 j and c=−7 i−5 ja) Find a+b+c b) Show that 3b−c is parallel to 3 i−2 j

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A105 Vectors

Unit vectors

WB9 choose which match

WB10 Point A is (4, 7) and point B is (9, 2)

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A105 Vectors Find vector A⃗B

WB11 a) If A is (2, 8) and B is (-3, 4) find the magnitude of A⃗Bb) If P is (-4, -3) and Q is (-6, 8) find the magnitude of P⃗Qc) Comment on your answers to a) and b)

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A105 Vectors WB12 Given that the point P has position vector 3 i−6 j and the point Q has position

vector −2 i−12 j a) Find the vector Q⃗Pb) Find |⃗PQ|

WB13 Given that the point point S has position vector 4 i+ j and the point T has position vector −3 i+7 j

a) Find the vector S⃗Tb) Find |⃗ST| giving your answer as a simplified surd

WB14 Given that the point A has position vector 3 i−6 j and the point B has position vector

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A105 Vectors −2 i−p j where pis a constant

a) Find the vector A⃗B in terms of pb) Given that |⃗AB|=4√6 find the two possible values of p showing all working

WB15Unit vectors

Find in exact form, unit vectors in the same direction as: a) a=9 i−12 j b) b=4 i+5 j c) a+b d) b−a

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A105 Vectors

WB16 Given that a=6 i+8 j, b=−2 i−4 j and c=2i+ ja) Find each of |a| |b| and |b+c| b) Find a unit vector in the direction of a−cc) Find a unit vector in the direction of 2b−c

WB17 In triangle ABC A⃗B=−3i+6 j and A⃗C=10 i−2 ja) Find the size of angle ∠BAC in degrees, to one decimal placeb) Find the exact value of the area of ⊿ ABC

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A105 Vectors

WB18 Given that the point A has position vector 5 i−2 j and A⃗B=3i−4 j a) Find the position vector of point Bb) Find |⃗OB|

Given that C is a point vertically above B and |⃗AC|=5 c) Find the coordinates of point C

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