Given that
a = 10 i + j and b = 8 i + 6 j
find the following.
Find a unit vector in the opposite direction to a.
i tried -10*i - j but it is not the right answer.
2006-08-30 17:24:34 · 7 answers · asked by zz06 3 in Science & Mathematics ➔ Mathematics
i got a hint from someone about why -10i-j is wrong
vector oppositely directed to another vector is obtained by multiplying by the scalar -1. To also make it a unit vector, divide by its length (which is not changed by multiplying by the scalar -1).
2006-08-30 17:44:19 · update #1
Your answer of -10i, -j is a vector in the opposite direction of a (= 10i, j), but it is not a *unit* vector. A unit vector is defined as a vector with a length equal to 1. Your “opposite” vector has a length of sqrt((-10)^2 + (-1)^2) = sqrt(101) . We can convert it to a unit vector by dividing both the x (i.e., “i”) and y (i.e., “j”) components by sqrt(101):
The correct answer is therefore (-10/sqrt(101)*i, -1/sqrt(101)*j)
2006-08-30 17:45:03 · answer #1 · answered by hfshaw 7 · 1⤊ 0⤋
A vector opposite to a is -a. Therefore -10i-j is one possible correct answer. If this is a multiple choice question any other vector in of the form -10ki - ki where k is a positive constant will work. For example -20 - 2j would also be opposite in direction to a.
2006-08-30 17:38:59 · answer #2 · answered by selket 3 · 0⤊ 1⤋
Of course -10*i - j is a vector opposite to the direction of 10*i + j. BUT it is NOT a unit vector.
A Unit Vector is the one with unit magnitude. So you have to divide it by its magnitude.
The magnitude of -10*i - j will be Sqr. Root [(-10)^2 + (-1) ^2]
i.e. Sqr. Root [ 100 + 1 ] = Sqr. Root [ 101 ] = 10.05 approx.
So Unit Vector in the opposite direction of "a" will be:
[-10*i -j ]/10.05 or -0.995*i - 0.0995*j
P.S.: Vector b = 8i + 6j is redundant - not used at all!
2006-08-30 18:13:33 · answer #3 · answered by quidwai 4 · 1⤊ 0⤋
As shown above, type vectors AB = B - A AC = C - A Then locate the bypass product v = AB x AC the portion of a parallogram is comparable to |AB x AC|; and the portion of the triangle is 0.5 that. So, no longer purely like the previous placed up, comprehend that the section if a million/2 of the size of this vector section = a million/2 |v| section = 15.3 instruments²
2016-11-06 03:07:45 · answer #4 · answered by shuey 4 · 0⤊ 0⤋
unit vector oppsite to a is
(-1)*(10i+j)/(101^0.5)
2006-08-30 17:39:45 · answer #5 · answered by lee_axil 1 · 1⤊ 0⤋
I don't know as if you can answer this question as there are 3 veriables and only two equations....???
2006-08-30 17:31:42 · answer #6 · answered by uncle.bubba 2 · 0⤊ 2⤋
j - 10i
2006-08-30 17:27:48 · answer #7 · answered by Anonymous · 0⤊ 1⤋