The vectors and are orthogonal True False Convert 3 3 to pol

The vectors and are orthogonal True False Convert (3, -3) to polar coordinates. (3squareroot2 middot 315*) (3.45*) (3squareroot2, 135*) (3, 135*)

( 19 )

given

dot product of two vectors is zero ,then they are orthogonal

( 4 , 5 ) and ( -10 , 8 )

==> < 4 , 5 > . < - 10 , 8 >

==> 4*-10 + 5* 8

==> - 40 + 40

==> 0

Therefore , given vectors are orthogonal

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( 20 )

given

( x , y ) = ( 3 , - 3 )

r^2 = x^2 + y^2

r^2 = ( 3)^2 + ( -3)^2

r^2 = 9 + 9

r = sqrt(18)

r = 3sqrt(2)

theta = tan^-1 ( y/x)

= tan^-1 ( - 3/ 3)

= tan^-1(-1)

it is in III quadrant

==> - 45

==> 180 - 45 ===> 135

( r , theta) = ( 3 sqrt(2) , 135 )