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please help me solve (from a review book)

1)If the magnitudes of vectors A and B are 5 and 12, respectively, then the magnitude of vector (b-a) cannot be:
A)5 B)7 C)10 D)12 E)17

Answer is A. Please explain why

2)If arccos(cos x) = 0, and x is between 0 and pi/2 (inclusive of those two values), then x could equal:
A)0 B)pi/6 C)pi/4 D)pi/3 E)pi/2

Answer: A. Explain

3) If n distinct planes intersect in a line, and another line L intersects one of these planes in a single plane, what is the LEAST number of these n planes that L could intersect?
A)n B)n-2 C)n-2 D)n/2 E)(n-1)/2

Answer: B. 'splain

4) In how many ways can ten people be divided into two groups, one with seven people and the other with three people? A)120 B)210 C)240 D)5040 E)14400

Answer is A. Please explain

By C0nfusion (C0nfusion) on Sunday, May 30, 2004 - 01:26 am: Edit

The vectors can be either +/- because it tells you the magnitudes of the vectors are 5 and 12. Therefore:
12-5 = 7
(-12)-5 = -17 (17)
12 - (-5) = 17
(-12) - (-5) = -7 (7)

and because the vectors can be at any angle to each other the magnitude of the subtraction of the two can be any number between 7 and 17

By Socalnick (Socalnick) on Sunday, May 30, 2004 - 01:34 am: Edit

1) A because if add/subtract the vectors the range of vectors you can have is 7<x<17 so the only impossible one is 5.

2) A because arccos(cosx)=n x=n

3)i dont kno but u must have wrote the problem wrong because the answer to b and c are the same

4) 10ncr3 or 10ncr7 because the remaining people would have to go into the other group 10ncr3*10ncr7 would be true if the events were independent

By Optimizerdad (Optimizerdad) on Sunday, May 30, 2004 - 07:46 am: Edit

I suspect that Q.3 should read
'3) If n distinct planes intersect in a line, and another line L intersects one of these planes in a single point, what is the LEAST number of these n planes that L could intersect?
A)n B)n-1 C)n-2 D)n/2 E)(n-1)/2 '

If the n planes intersect, then no plane is parallel to any of the others. A line will not intersect a plane only if it is parallel to the plane; if line L is parallel to one of the n planes, it cannot therefore be parallel to any of the others, and must intersect all of the remaining (n-1) planes. Answer is B).

(... I think :-)

By Flchagani (Flchagani) on Sunday, May 30, 2004 - 11:14 am: Edit

DOH!!!!!!!!!!!!!!

Sorry about number 3 y'all. The CORRECT choices were, as Optimizerdad pointed out:

A)n B)n-1 C)n-2 D)n/2 E)(n-1)/2

By Socalnick (Socalnick) on Sunday, May 30, 2004 - 01:36 pm: Edit

oh for number three if the planes can not be parallel to each other that means the line can only be parallel to 1 of the planes.

By Joshjmgs (Joshjmgs) on Sunday, May 30, 2004 - 08:20 pm: Edit

For #2, 'Plug it in, plug it in ^^'
Takes 2 seconds.
But remember Radian mode!!!!
I think everything is in radian mode unless otherwise noted with the small degree sign (a circle in the upper-right corner)

By Conker (Conker) on Monday, May 31, 2004 - 05:56 am: Edit

What does it mean to "intersect in a line"?

By Optimizerdad (Optimizerdad) on Monday, May 31, 2004 - 08:41 am: Edit

Think of the pages of an open book as representing planes. Some pages will be nearly horizontal, others will be lifted up slightly, still others will be nearly vertical. Each is at a different angle, but they all intersect along the spine of the book, which would be the 'line'.

An example of planes that do *not* intersect in a line would be the x /y / z planes in three_dimensional geometry; they intersect at a single point (0,0,0) rather than along a line.