Vectors!!!

[Ressha]

Given v = 2i + 3j and w = 2i + j. Point P is (3, -3) and point Q is (9,2). Given PQ = hv + kw where h and k are constants. Find the values of h and k.

 

[Deleted member 4993]

Given v = 2i + 3j and w = 2i + j. Point P is (3, -3) and point Q is (9,2). Given PQ = hv + kw where h and k are constants. Find the values of h and k.

Write the description of the vector PQ from the given co-ordinates of P & Q..................................(1)

Also write PQ = hv + kw = h*(2i + 3j) + k*(2i + j) ....................................(2)

Now equate i and j components of (1) and (2)

continue.....

Please show us what you have tried and exactly where you are stuck.

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[Ressha]

Can you please show me on how to write the description of the vector PQ??? Please...

 

[Deleted member 4993]

Can you please show me on how to write the description of the vector PQ??? Please...

If

the coordinates of P is (x₁, y₁) and

the coordinates of Q is (x₂, y₂)

Then the cartesian description of the vector PQ (from P to Q) is:

PQ = (x₂ - x₁) i + (y₂ - y₁) j

continue......

 

[Ressha]

Thank you so much for helping me to solve this question.

 

[Ressha]

I’ve tried but still stuck in here....

 

[Deleted member 4993]

Write the description of the vector PQ from the given co-ordinates of P & Q..................................(1)

Also write PQ = hv + kw = h*(2i + 3j) + k*(2i + j) ....................................(2)

Now equate i and j components of (1) and (2)

Good work. So you found that

6i + 5j = h*(2i + 3j) + k * (-2i + j)

6i + 5j = h*2i + h*3j + k * (-2i )+ j*k

6i + 5j = h*2i + k * (-2i )+ j*k + h*3j = i * (2h - 2k) + j * (3h + k)

Now equate 'i' and 'j' components. That will give you two equations involving two unknown. Solve.....