Question

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

Answer 1

`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>`

Answer 2

`< 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))`