How do you find #u=1/2v-w+2z# given v=<4,-3,5>, w=<2,6,-1> and z=<3,0,4>?

2 Answers
May 19, 2017

#u=<6,-15/2,23/2>#

Explanation:

As #v=<4,-3,5>, w=<2,6,-1># and #z=<3,0,4>#

#u=1/2v-w+2z#

#=<(1/2xx4-2+2xx3),(1/2(-3)-6+2xx0),(1/2xx5-(-1)+2xx4)>#

#=<6,-15/2,23/2>#

May 19, 2017

#< 6,-15/2,23/2 >#

Explanation:

#"Notation" < x,y,z > -=((x),(y),(z))#

To multiply a vector by a scalar quantity, multiply each component of the vector by the scalar.

#color(red)(a)((x),(y),(z))=((color(red)(a)x),(color(red)(a)y),(color(red)(a)z))#

To add/subtract vectors, add/subtract corresponding components of the vectors.

#((x_1),(y_1),(z_1))+-((x_2),(y_2),(z_2))=((x_1+-x_2),(y_1+-y_2),(z_1+-z_2))#

#rArr1/2ulv-ulw+2ulz#

#=1/2((4),(-3),(5))-((2),(6),(-1))+2((3),(0),(4))#

#=((2),(-3/2),(5/2))-((2),(6),(-1))+((6),(0),(8))#

#=((6),(-15/2),(23/2))#