Two birds are flying towards their nest, which is in a tree.

Relative to a fixed origin, the flight path of each bird is modelled by a straight line.

In the model, the equation for the flight path of the first bird is

r1 = (-i + 5j + 2k) + λ(2i + aj)

and the equation for the flight path of the second bird is

r2 = (4i - j + 3k) + μ( j - k)

where λ and μ are scalar parameters and a is a constant.

In the model, the angle between the birds’ flight paths is 120°

(a) Determine the value of a.

(b) Verify that, according to the model, there is a common point on the flight paths of

the two birds and find the coordinates of this common point.

The position of the nest is modelled as being at this common point.

The tree containing the nest is in a park.

The ground level of the park is modelled by the plane with equation

2x – 3y + z = 2

(c) Hence determine the shortest distance from the nest to the ground level of the park.

(d) By considering the model, comment on whether your answer to part (c) is reliable,

giving a reason for your answer.

This is the question and I get the answer for a, however when a^2 is 4, it only accepts -2, can anyone explain why?

Relative to a fixed origin, the flight path of each bird is modelled by a straight line.

In the model, the equation for the flight path of the first bird is

r1 = (-i + 5j + 2k) + λ(2i + aj)

and the equation for the flight path of the second bird is

r2 = (4i - j + 3k) + μ( j - k)

where λ and μ are scalar parameters and a is a constant.

In the model, the angle between the birds’ flight paths is 120°

(a) Determine the value of a.

(b) Verify that, according to the model, there is a common point on the flight paths of

the two birds and find the coordinates of this common point.

The position of the nest is modelled as being at this common point.

The tree containing the nest is in a park.

The ground level of the park is modelled by the plane with equation

2x – 3y + z = 2

(c) Hence determine the shortest distance from the nest to the ground level of the park.

(d) By considering the model, comment on whether your answer to part (c) is reliable,

giving a reason for your answer.

This is the question and I get the answer for a, however when a^2 is 4, it only accepts -2, can anyone explain why?

Original post by SGDumpling

Two birds are flying towards their nest, which is in a tree.

Relative to a fixed origin, the flight path of each bird is modelled by a straight line.

In the model, the equation for the flight path of the first bird is

r1 = (-i + 5j + 2k) + λ(2i + aj)

and the equation for the flight path of the second bird is

r2 = (4i - j + 3k) + μ( j - k)

where λ and μ are scalar parameters and a is a constant.

In the model, the angle between the birds’ flight paths is 120°

(a) Determine the value of a.

(b) Verify that, according to the model, there is a common point on the flight paths of

the two birds and find the coordinates of this common point.

The position of the nest is modelled as being at this common point.

The tree containing the nest is in a park.

The ground level of the park is modelled by the plane with equation

2x – 3y + z = 2

(c) Hence determine the shortest distance from the nest to the ground level of the park.

(d) By considering the model, comment on whether your answer to part (c) is reliable,

giving a reason for your answer.

This is the question and I get the answer for a, however when a^2 is 4, it only accepts -2, can anyone explain why?

Relative to a fixed origin, the flight path of each bird is modelled by a straight line.

In the model, the equation for the flight path of the first bird is

r1 = (-i + 5j + 2k) + λ(2i + aj)

and the equation for the flight path of the second bird is

r2 = (4i - j + 3k) + μ( j - k)

where λ and μ are scalar parameters and a is a constant.

In the model, the angle between the birds’ flight paths is 120°

(a) Determine the value of a.

(b) Verify that, according to the model, there is a common point on the flight paths of

the two birds and find the coordinates of this common point.

The position of the nest is modelled as being at this common point.

The tree containing the nest is in a park.

The ground level of the park is modelled by the plane with equation

2x – 3y + z = 2

(c) Hence determine the shortest distance from the nest to the ground level of the park.

(d) By considering the model, comment on whether your answer to part (c) is reliable,

giving a reason for your answer.

This is the question and I get the answer for a, however when a^2 is 4, it only accepts -2, can anyone explain why?

(edited 2 months ago)

Original post by mqb2766

When a=2, the angle is 60, not 120. It would help to see what you did if you for the extraneous solution a=2.

Original post by SGDumpling

oh my god thank you so much! i didnt think of that but if i did plug 2 into the equation, cosθ is 1/2 which is 60 degrees. Thank you so much

(edited 2 months ago)

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