I've spent two hours trying to do this, but I cant figure a way out . We've just started the Gr. 12 Geometry and Discrete Mathematics and so far we've done dot product/cross product of vectors in 2,3 dimentions in cartesian and algebraic form

 

The sundial shown on the bottom works on the principle that the sun casts a shadow from a central projecting pointer onto the surface of a calibrated circle. The edge of the shadow is used to indicate the time of the day. A coordinate system can be placed on this object so that A is at the origin. A(0,0,0) and the coordinates of B and K are B(0,8,3) and C(-4,4,0).

 

Determine the following:

 

a) The magnitude of the vector projection of the edge of the pointer AB onto the calibration line AC

 

b) The size of Angle BAC

 

 

Any help would be greately appreciated

Have you been taught unit vectors? That's what you should use, as far as I can see.

You are given A(0,0,0) B(0,8,3) and C(-4,4,0).

 

1) AB dot AC

 

2) (AC)*(AB)*cos(BAC) = AB dot AC

 

AB = 8 j + 3 k

AC = -4 i + 4 j

AB = sqrt(8^2 + 3^2) = sqrt(64+9) = sqrt(73)

AC = sqrt((-4)^2 + 4^2) = sqrt(16 + 16) = sqrt(32)

 

AB dot AC = 32

or if you use unit vectors it should be.. 0.6621

 

1) 0.6621

2) angle BAC = cos^-1 ( 32/48.33) = 48.541