H2 Maths Vectors question

jonchao72 SG

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 SG

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

jonchao72 SG

yep did that, thx!

chocolates-xed SG

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 SG

Hi,

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

Thanks!

Cheers,
Wen Shih

chocolates-xed SG

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

wee_ws SG

Hi,

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

Cheers,
Wen Shih

chocolates-xed SG

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

wee_ws SG

Hi,

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

Cheers,
Wen Shih

chocolates-xed SG

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

wee_ws SG

Hi,

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

Cheers,
Wen Shih

chocolates-xed SG

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 SG

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

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

wee_ws SG

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 SG

ok thanks understand now.(:

chocolates-xed SG

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 SG

Hi,

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

Thanks!

Cheers,
Wen Shih