Question

Chap 6

Answer 1

?

Answer 2

http://prntscr.com/4uugkg

Answer 3

Can you please help to sketch the situation ?

Answer 4

@waterineyes

Answer 5

Higher Authorities to be consulted.. :P

Answer 6

ok

Answer 7

@ganeshie8

Answer 8

You may refer this.. http://prntscr.com/4uujr2

Answer 9

basically we need two things to represnet a line using vectors :
1) direction vector (direction in which the line shoots)
2) position vector (starting point)

Answer 10

once you have above both, you can write the equation of line as :
`position vector` + t `direction vector`

Answer 11

Notice that you're already given `position vector` : 3i-2j

Answer 12

lets see how to find the direction vector

Answer 13

clear so far ?

Answer 14

yes

Answer 15

two vectors are perpendicular means, their `dot product` equals 0, yes ?

Answer 16

That applies for scalar product rite

Answer 17

yes
say the required direction vector is `ai + bj`,
since this is perpendivular to the given line with direction vector `i - 2j`

the scalar or dot product has to be 0

Answer 18

(ai+bj) . (i - 2j) = 0

a - 2b = 0

a = 2b

when b=1, a =2
so a direction vector can be `2i + 1j`

Answer 19

now that you have both position and direction vectors, you can write the equaiton of line :

`position vector` + t `direction vector`

Answer 20

`(3i - 2j)` + t `(2i+1j)`

Answer 21

How to know that I need to use dot product instead of vector product

Answer 22

this is a very important result when you start learning vector geometry :

\[\large \text{two vectors are perpendicular} \iff \text{dot prodyct = 0}\]

Answer 23

*product

Answer 24

it is always `dot product` with problems involving `perpendicular` lines/vectors

Answer 25

Okay

Answer 26

Can you sketch a diagram based on the question

Answer 27

First of all notice that the vectors in questions have "two" components,
that means the vectors belong to 2-dimensional xy plane

Answer 28

the one you're used to from highschool

Answer 29

lets first draw the given line : `(i - j) + t(i-2j) `

Answer 30

can you plot the head of `position vector `?