Referring to the picture find u v and a given u 120mhr v

Referring to the picture, find |u + v| and a given |u| = 120m/hr. |v| = 85m/hr and the angle between the two vectors is 72 degree. Find the standard vector for the vector AB^vector where A = (2, 7) and B = (5, -1). A. Find the magnitude of v^vector = B. Find a unit vector in the same direction as v^vector. C. Find a vector of length 3 that has the same direction as v^vector. Sketch A boat capable of traveling 12 knots on still water has a compass heading of 250 degree while crossing a river. If river is flowing at 3 knots at a heading of 180 degree, what is the velocity (magnitude and direction) of the boat relative to the river bottom? Express the vector as a linear combination of the i and j vectors. If u = 3i + 8j and v = -2i + j, then find 2u - 3v. Referring to the picture, write the vector u as a linear combination of the unit vectors i and j.

Solution

( 8 )

given

u = 3 i + 8j

v = - 2i + j

2 u = 2 ( 3 i + 8 j ) ==> 6 i + 16 j

3v = 3 ( - 2 i + j ) = - 6 i + 3 j

2 u - 3 v ==> 6 i + 16 j - ( - 6 i + 3 j )

==> 12 i + 13 j

( 3 )

given

A = ( 2 , 7 ) , B = ( 5 , - 1 0 )

AB = ( 5 - 2 ) i + ( - 10 - 7 ) j

= 3 i - 17 j

( 2 )

given | u | = 120 , | v| = 85 , theta = 72⁰

==> u . v = | u |  | v| cos( theta)

==> 120*85 cos(72⁰ ) ==> 3151.9733

|u + v |^2 = (u+v)(u+v)

= uu+vv+2(uv)

u^2+ v^2 + 2(uv)

|u + v | = sqrt( u^2+ v^2 + 2(uv) )

==> sqrt( 120^2 + 85^2 + 2 (3151.9733 ) )

|u + v | ===> 167.119558