1. Find the component form of the vector representing the velocity of a boat traveling at 8 knots, or nautical miles per hour, with a bearing of N 53-degrees W.

2. A force of 703 pounds is needed to push a stalled car up a hill inclined at an angle of 16-degrees to the horizontal. Find the weight of the car. Ignore friction.

3. The vectors U and V are orthogonal. Find the value of a.
U= {a,-7}, v= {42,-30}

4. A horizontal force of 80 pounds is applied to an object as it is pushed up a ramp that is 13 feet long. Find the work done if the ramp is inclined at an angle of 40-degrees above the horizontal.

5. Find the indicated roots of the complex number. Fifth roots of 32.

1. Find the component form of the vector representing the velocity of a boat traveling at 8 knots, or nautical miles per hour, with a bearing of N 53-degrees W.
Using i represent the N direction and j represent the W direction, then we got the vector ...

Solution Summary

This shows how to work on word problems involving vectors and force.

Linear Algebra - Vector Spaces. ... Show that P, with the usual addition and scalar multiplication of functions, forms a vector space. I'm just no good at proofs. ...

... 1. What are Vectors (or vector quantities) and how do they differ from Scalars (or scalar quantities)? ...Vector sum of the two vectors is defined as follows: B. ...

Matrices, Vector Spaces and Zero Vectors. ... Matrices, Vector Spaces and Zero Vectors are investigated. The solution is detailed and well presented. ...

... 5. Knowing Vectors A and B as given above and given a vector C = (-200) xunit vector + (-160) yunit vector. C is also measured in grams for its magnitude. ...

... By linking the vectors "head to tail" the summation yields a vector from the tail of the first vector to the head of the last vector (The resultant vector is ...

... The questions pertain to trigonometry, scalars and vectors, vector addition and subtraction, components of vector, and addition of vectors by means of ...

...Vector Space A non-empty set of vectors V is called a vector space over a scalar field when the vector addition and scalar multiplication operations satisfy ...

... the basis for the vector subspace V, so that one can write: ( 25) and ( 26) This means that any linear combination of these vectors will give a vector in V and ...