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Gloomycus

09-20-2002, 12:32 PM

I'm bored, so I thought I would post a problem for you people to solve.

Find a unit vector that is perpendicular to both vectors a' = (-3,-1,5) and b' = (1,4,-3) and that makes an obtuse angle with the positive z-axis.

ericlin

09-20-2002, 02:26 PM

//a' = (-3,-1,5) and b' = (1,4,-3)

x1 = -3;

y1 = -1;

z1 = 5;

x2 = 1;

y2 = 4;

z2 = -3;

z = 1;

x = (z1*y2-z2*y1)/(x2*y1-x1*y2);

y = (z2*x1-z1*x2)/(x2*y1-x1*y2);

distance = Math.sqrt(x*x+y*y+z*z);

x /= distance;

y /= distance;

z /= distance;

trace(x);

//0.823652691289566

trace(y);

//0.193800633244604

trace(z);

//0.53295174142266

Am I right ?

muckyMuckMan

09-20-2002, 04:26 PM

How about this?

a = <-3, -1, 5>

b = <1, 4, -3>

// Cross Product

a X b = -17i - 4j - 11k

// Magnitude of Cross Product

||a X b|| = sqrt(426)

// Unit vector

a X b

----------

||a X b||

17 4 11

= - ---------i - --------j - --------k

sqrt(426) sqrt(426) sqrt(426)

This vector makes an obtuse angle from the positive z-axis since it's z-component is negative (Is that sound reasoning?) Am I right?

mike_flashmx

10-18-2002, 09:54 PM

Deleted.