Posted by Steve on Sunday, November 2, 2008 at 2:39pm.
A=i –2j B=-3i+j How do I find the component of A that is perpendicular to B in vector form?
- Vectors - Damon, Sunday, November 2, 2008 at 5:57pm
A = i - 2 j so |A| = sqrt 5
B = -3 i + j so |B| = sqrt 10
The magnitude of the cross product A x B is |A| |B| sin T
where T is the angle between the vectors.
i j k
1 -2 0
-3 1 0 --> -5 k
so the magnitude of the cross product is 5
sqrt 5 * sqrt 10 * sin T = 5
5 sqrt 2 * sin T = 5
sin T = 1/sqrt 2
The component of A perpendicular to B, call it R, therefore has magnitude sqrt 5 /sqrt 2
We know that it is perpendicular to B so
B dot R has magnitude = 0
Rx Bx + RyBy = 0
Rx(-3)+ Ry(1) = 0
so Ry = 3 Rx
so call it
R = c Rx + 3c Ry where c is a constant
magnitude = c sqrt (10)
which has to be sqrt 5/sqrt 2
so c sqrt 10 = sqrt 5/sqrt 2
c = sqrt 5 /(sqrt 2*sqrt 2 * sqrt 5)
c = 1/2 but it could be negative
so our vector is
R = (1/2) i + (3/2) j
R = -(1/2) i - (3/2) j
looking at a sketch of the vectors, use the second one but both are valid.
Answer this Question
More Related Questions
- Physics - You are given vectors A = 5.0i - 6.5j and B = -2.5i + 7.0j. A third ...
- Math: Trig - Help with vectors, please. Thanks 1) Express point in rectangular ...
- Physics - The two vectors a and b have equal magnitudes(on an x-y plane vector a...
- Math: Vectors - Find any vector w that is perpendicular to both vector "u = 3j...
- maths - Given that vector c and vector d are non zero vectors such that vector c...
- physics [vectors] - The concept i get, but somehow i just can't execute this ...
- Physics - You are given vectors A = 5.0i - 6.5j & B = -3.5i + 7.0j. A third ...
- science (physics) Need to solve this today please - (a) Express the vectors A, B...
- Physics - Vectors A and B are added to produce C, that is A+B=C. If B=-5x+5y and...
- physics - The drawing shows a force vector vector F that has a magnitude of 600 ...