Question

Chap 6.6

Answer 1

Find the acute angle between the line r= 3i - 2j + lambda (i + j + k ) and
x-3/2= y-2/-3= z-1/4

Answer 2

@ganeshie8

Answer 3

angle between lines is same as the angle between their `direction vectors`

Answer 4

ganeshie i need your help

Answer 5

for the first line,
direction vector = i+j+k = (1, 1, 1)

for the second line,
direction vector = (2, -3, 4)

Answer 6

u dere i need ur help

Answer 7

pm me factor

Answer 8

okee hold a sex

Answer 9

find the angle between those vectors using dot product

Answer 10

scalar product ?

Answer 11

yes

a.b = |a| |b| cos(theta)

Answer 12

you can find angle using abvoe formula

Answer 13

How do you determine this
for the first line,
direction vector = i+j+k = (1, 1, 1)

for the second line,
direction vector = (2, -3, 4)

Answer 14

r= 3i - 2j + lambda (i + j + k )

Answer 15

i pm ed u

Answer 16

Okay, will try now..

Answer 17

Notice that the direction vector is getting multiplied by a scalar `lambda` and each value of this gives you a point on the line which shoots in the direction i+j+k

Answer 18

in short : whatever gets multiplied by this parameter is the direction vector

Answer 19

ok

Answer 20

a = (1,1,1)
b = (2, -3, 4)

your goal is to find the angle between them

Answer 21

So, a.b = (1+1+1) x ( 2-3+4) ?

Answer 22

I mean I can substitute them with a.b

Answer 23

a = (1,1,1)
b = (2, -3, 4)

a.b = 1*2 + 1(-3) + 1*4

Answer 24

set that equal to `|a| |b| cos(\theta)` and solve `\theta`

Answer 25

like this