# Can anyone help me with this vector question?

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A pipeline is to be fitted beneath a road as represented in the image. All lengths are in meters.

A) Calculate the length of the pipe AB. Use diagrams to support your answer where required.

B) The section BC is to be drilled in the direction 3i + 4j + k. Find the angle between the sections *AB* and *BC*.

C) The pipe ends at point C (a,b,0). Give a vector equation of the line *BC*. Hence find *a* and *b*.

A pipeline is to be fitted beneath a road as represented in the image. All lengths are in meters.

A) Calculate the length of the pipe AB. Use diagrams to support your answer where required.

B) The section BC is to be drilled in the direction 3i + 4j + k. Find the angle between the sections *AB* and *BC*.

C) The pipe ends at point C (a,b,0). Give a vector equation of the line *BC*. Hence find *a* and *b*.

##### 1 Answer

#### Answer:

See below.

#### Explanation:

Given

we have

Segment

now with

and finally

and solving we get