- #1

CaliforniaRoll88

- 35

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- Homework Statement
- A vector field is specified as ##\vec G=24xy\hat a_x+12(x^2+2)\hat a_y+18z^2\hat a_z##. Given two points, ##P(1,2-1)## and ##Q(-2,1,3)##, find (a) ##\vec G## at ##P##; (b) a unit vector in the direction of ##\vec G## at ##Q##; (c) a unit vector directed from ##Q## toward ##P##; (d) the equation of the surface on which ##|\vec G|=60##

answers:

(a) ##48\hat a_x + 36\hat a_y + 18\hat a_z##

(b) ##−0.26\hat a_x + 0.39\hat a_y + 0.88\hat a_z##

(c) ##0.59\hat a_x + 0.20\hat a_y − 0.78\hat a_z##

(d) ##100 = 16x^2 y^2 + 4x^4 + 16x^2 + 16 + 9z^4##

Source: Problem 1.5; Engineering Electromagnetics, 8th Edition, William Hayt, John Buck

- Relevant Equations
- ##\vec G=24xy\hat a_x+12(x^2+2)\hat a_y+18z^2\hat a_z##

(a)

##\vec G=24xy\hat a_x+12(x^2+2)\hat a_y+18z^2\hat a_z## @ ##P(1,2-1)##

##\vec G=24(1)(2)\hat a_x+12(1^2+2)\hat a_y+18(-1)^2\hat a_z##

##\vec G=48\hat a_x+36\hat a_y+18\hat a_z##

(b)

I am not sure how to get this part started. Could someone point me in the right direction?

##\vec G=24xy\hat a_x+12(x^2+2)\hat a_y+18z^2\hat a_z## @ ##P(1,2-1)##

##\vec G=24(1)(2)\hat a_x+12(1^2+2)\hat a_y+18(-1)^2\hat a_z##

##\vec G=48\hat a_x+36\hat a_y+18\hat a_z##

(b)

I am not sure how to get this part started. Could someone point me in the right direction?