H2 Maths Vectors question

• jonchao72

  10 May 09, 22:10

  erm, how do i show that two planes are parallel to each other

  one plane is in parametric form while the other is in vector equation form

  thx!

• eagle

  11 May 09, 00:12

  find the n vector perpendicular to both planes and show that the 2 vectors are parallel

• jonchao72

  12 May 09, 21:59

  yep did that, thx!

• chocolates-xed

  22 May 09, 20:59

  how to do this qn? quite urgent. been cracking brains.

  Given this line r = (3 -2 2) + t(-4 3 1) is perpendicular to the vecor i + 2j + pk. Find the value of P.

• wee_ws

  22 May 09, 22:09

  Hi,

    Consider the scalar product of the line's direction vector and i + 2j + pk?

    Thanks!

  Cheers,
  Wen Shih

• chocolates-xed

  22 May 09, 22:15

  the dot product of the direction vector and i + 2j + pk will = 0?

• wee_ws

  22 May 09, 22:18

  Hi,

    Both the line and given vector are perpendicular yes? So what does the scalar product give? Thanks!

  Cheers,
  Wen Shih

• chocolates-xed

  22 May 09, 22:20

  yea, its perpendicular. the product is (-4 6 p)

• wee_ws

  22 May 09, 22:22

  Hi,

    Shouldn't scalar product be -4 + 6 + p?

  Cheers,
  Wen Shih

• chocolates-xed

  22 May 09, 22:23

  oh ya sorry sorry. then what must i do after that?

• wee_ws

  22 May 09, 22:25

  Hi,

    When two vectors are perpendicular, do you recall that the scalar product is a special value?

  Cheers,
  Wen Shih

• chocolates-xed

  22 May 09, 22:27

  oh get it! -4+6+p = 0 -> p=-2

  THANKS!!!(:

  oh ya. can explain why must use direction vector to find scalar product?

  why can't use the same way as for parallel?

• eagle

  22 May 09, 22:28

  Originally posted by chocolates-xed:

  oh ya sorry sorry. then what must i do after that?

  Originally posted by chocolates-xed:

  the dot product of the direction vector and i + 2j + pk will = 0?

  

• wee_ws

  22 May 09, 22:33

  Hi,

    Because the direction vector is the most important distinguishing feature of any line.

    When another line L2 is parallel to a given line L1 with direction vector d, L2 has the same direction vector d. The only difference between L1 and L2 is the point each line passes through.

    Thanks!

  Cheers,
  Wen Shih 

• chocolates-xed

  22 May 09, 22:39

  ok thanks understand now.(:

• chocolates-xed

  22 May 09, 22:46

  relative to the origin O, the points A, B and C have position vectors given a=.... b=.... c=......

  the qn asks: Find the vector equation of the line l that passes through point A and is parallel to the vector a

   

  does is mean i need to find vector AB ?

  then use the vector equation r = vector OA + (lumda) vector AB ??

• wee_ws

  23 May 09, 07:17

  Hi,

    The direction vector of the line is the vector a. The point that it passes through is OA.

    Thanks!

  Cheers,
  Wen Shih