i) Since v₁ is parallel to vector w, let vector v₁ = 2ti + tj, where t is a scalar.
and let v₂ be = ai + bj
ii) Given: v₁ + v₂ = v
==> (2t + a)i + (t + b)j = -3i + 2j
Equating the corresponding components, [two vectors are said to be equal, if and only if their corresponding components are equal]
2t + a = -3 ---------- (1) and t + b = 2 ------------ (2)
iii) Another given data is: v₂ orthogonal to w; so v₂.w = 0
==> (ai + bj).(2i + j) = 0
==> 2a + b = 0 ---------- (3)
iv) Solving (1), (2) & (3): a = -7/5; b = 14/5 and t = -4/5
So vector v₁ = -(4/5)(2i + j)
and vector v₂ = (-7/5)i + (14/5)j
If you are satisfied with the above solution kindly acknowledge, need not be BA - just with a simple word of Thanks. More than 90% of the persons who ask question are not even obliged to acknowledge with a simple thanks, which I believe keeps many from providing solutions.
REQUEST: Those who wish to rate this solution with TD, you are welcome; but only one request, kindly give the reasons for the same in the comments column, which will make me to correct mistake and learn more. Thanks for your cooperation.
Comments
i) Since v₁ is parallel to vector w, let vector v₁ = 2ti + tj, where t is a scalar.
and let v₂ be = ai + bj
ii) Given: v₁ + v₂ = v
==> (2t + a)i + (t + b)j = -3i + 2j
Equating the corresponding components, [two vectors are said to be equal, if and only if their corresponding components are equal]
2t + a = -3 ---------- (1) and t + b = 2 ------------ (2)
iii) Another given data is: v₂ orthogonal to w; so v₂.w = 0
==> (ai + bj).(2i + j) = 0
==> 2a + b = 0 ---------- (3)
iv) Solving (1), (2) & (3): a = -7/5; b = 14/5 and t = -4/5
So vector v₁ = -(4/5)(2i + j)
and vector v₂ = (-7/5)i + (14/5)j
If you are satisfied with the above solution kindly acknowledge, need not be BA - just with a simple word of Thanks. More than 90% of the persons who ask question are not even obliged to acknowledge with a simple thanks, which I believe keeps many from providing solutions.
REQUEST: Those who wish to rate this solution with TD, you are welcome; but only one request, kindly give the reasons for the same in the comments column, which will make me to correct mistake and learn more. Thanks for your cooperation.