The angle between the vectors a=3i-4j, and b=4i+3j,?

Question

a) 0degrees b)90degrees c)180degrees d)45degrees

Answer 1

a . b = |a| |b| cos θ
(12 - 12) = (5) (5) cos θ
cos θ = 0
θ = 90°
OPTION b)

Answer 2

It's 90 degrees, because a dot b = 0.
In general a dot b = |a| |b| cos t,
where t is the angle between the vectors.

Answer 3

Both vectors can be described by:
a = (3, -4)
b = (4, 3)

The dot product of two vectors equals the product of the vectors lengths times the cos of the angle between them. Or:

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

a (dot) b
= (3, -4) (dot) (4, 3)
= (3*4) + (-4*3)
= (12) + (-12)
= 0

The only way for |a||b|cos(theta) to equal zero is if cos(theta) is equal to zero.

cos(theta) = 0
theta = cos^-1(0)
theta = 90 degrees

Answer 4

Given:
a=3i-4j
b=4i+3j

Here ,
a1 = 3 a2= -4
b1=4 b2= 3

Formula:

Angle between two vectors, THETA: cos-1{ [(a1*b1) + (a2*b2)]/(|a|*|b|) }

|a| = SQRT [ a1^2 + a2^2 ]
= SQRT [ 3^2 + (-4)^2 ]
=SQRT [ 9+16 ]
=SQRT (25)
|a| = 5

Similiarly,

|b| = SQRT [ b1^2 +ba2^2 ]
= SQRT [ 4^2 + 3)^2 ]
=SQRT [ 16+9 ]
=SQRT (25)
|b| = 5

Therefore, Theta = cos-1{ [(3*4) + (-4*3)]/(5*5) }
= cos-1{ [(3*4) + (-4*3)]/(5*5) }
= cos-1{ [12-12] / 25 }
= cos-1{ 0 }
Theta = 90 degrees

Answer 5

the dot product of the two vectors is 0.

thus the two vectors are perpendicular.

the angle between them is 90°

§

Answer 6

90 degrees

Answer 7

a.b=3.4-4.3
=12-12
=0
so Cos( x)=0
=Cos90degrees
so x=90degrees
hence 'b' is the right answer.