What's the difference between dot product and cross product of vector?

What's the difference between dot product and cross product of vector?

Distinguish dot product from cross product
Dot product is also called inner product and scalar product of vector. As the name suggests, the result is a number
Vector a · vector b = |a|b|cos
In physics, the work of known force and displacement is actually the inner product of vector F and vector s, that is, point multiplication
Cross product, also known as the vector product, vector product. As the name suggests, the result is a vector, remember that the vector is C
|Vector C | = | vector a × vector B | = | - a | - B | - Sin
The direction of vector C is perpendicular to the plane of a and B, and the direction should be judged by the "right hand rule" (the four fingers of the right hand first represent the direction of vector a, and then the fingers swing towards the palm of the hand to the direction of vector B, and the direction pointed by the thumb is the direction of vector C)
therefore
The outer product of a vector does not obey the multiplicative commutation rate because
Vector a × vector b = - vector B × vector a
In physics, if we know the force and the arm of force, the moment is the outer product of vector
The vector is represented by coordinates (three-dimensional vector),
If vector a = (A1, B1, C1), vector b = (A2, B2, C2),
be
Vector a · vector b = A1A2 + b1b2 + C1C2
Vector a × vector b=
| i j k|
|a1 b1 c1|
|a2 b2 c2|
=(b1c2-b2c1,c1a2-a1c2,a1b2-a2b1)
(I, J and K are the unit vectors of three mutually perpendicular coordinate axes in space respectively)

109 degrees 11 minutes 4 seconds - 50 degrees 50 minutes 34 seconds 23 degrees 41 minutes 34 seconds + 36 degrees 18 minutes 26 seconds 180 degrees - (48 degrees 39 minutes 40 seconds + 67 degrees 41 minutes 35 seconds)

109 degrees 11 minutes 4 seconds - 50 degrees 50 minutes 34 seconds = 58 degrees 20 minutes 30 seconds
23 degrees 41 minutes 34 seconds + 36 degrees 18 minutes 26 seconds = 60 degrees 180 degrees - (48 degrees 39 minutes 40 seconds + 67 degrees 41 minutes 35 seconds) = 43 degrees 38 minutes 45 seconds

Solve the equation 4x-1.6 = 21

4x=21.6+1.6
4x=23.2
x=23.2/4
x=5.8

18.8 - two thirds - 3.8 - one third?

18.8 - two thirds - 3.8 - one third
=(18.8-3.8)-(2/3 +1/3)
=15-1
=14

In the triangle ABC, call a, B, C, the opposite side is a, B, C, and C = 3 / 4, Sina = √ 5 / 5, find the value of cosa, SINB

∵ Sina = √ 5 / 5 ＜ 1 / 20 ＜ a ＜ π / 6 or 5 π / 6 ＜ a ＜ π: C = π / 4 ∵ a ＜ π - π / 4 = 3 π / 4 ∵ 0 ＜ a ＜ π / 6 ∵ cosa = √ (1-sin ^ 2a) = 2 √ 5 / 5sinb = sin (π - A-C) = sin (a + C) = sinacosc + cosasinc = √ 5 / 5 * √ 2 / 2 + 2 √ 5 / 5 * √ 2 / 2 = 3 √ 10 / 10

Natural number n = 123456789101112 2008 is a new year______ Number of digits

Because there are nine single digit numbers 1-9, 90 double digit numbers 10-99, 900 three digit numbers 100-999, four digit numbers 1000-2008, 2008-1000 + 1 = 1009, 9 + 90 × 2 + 900 × 3 + 1009 × 49 + 180 + 2700 + 4036, = 6925, natural number n = 123456789101112 2008 is a 692

As shown in the figure, in two concentric circles with o as the center, the chord ab of the big circle intersects the small circle at two points c and D

For OE ⊥ AB, then AE = be, CE = De, so be-de = ae-ce; that is, AC = BD

Factorization (17 6:28:25)
Y-2x + 1 is a factor of 4xy-4x2-y2-k, then the value of K is ()
 

k=-1
Let another factor of 4xy-4x2-y2-k be ax + by + C. then (y-2x + 1) * (AX + by + C) = 4xy-4x2-y2-k
It unfolds well
（a-2b）xy-2ax2+by2+(b+c)y+(a-2c)x+c=4xy-4x2-y2-k
If the corresponding coefficients are equal, it can be solved
a=2,b=-1,c=1,k=-1

It is known that, as shown in the figure, in △ ABC, the bisector of ∠ ABC and ∠ ACB intersects at point o

It is proved that: the bisector of ∵ ABC and ∵ ACB intersects at point O, ∵ OBC = 12 ∵ ABC, ∵ OCB = 12 ∵ ACB, ∵ OBC + ∵ OCB = 12 (∵ ABC + ∵ ACB). In △ OBC, ∵ BOC = 180 ° - (∵ OBC + ∵ OCB) = 180 ° - 12 (? ABC + ? ACB) = 180 ° - 12 (180 ° - a) = 90 ° + 12 ? a

99+11×19+11×80______ ．

99 + 11 × 19 + 11 × 80 = 99 + (19 + 80) × 11, = 99 + 99 × 11, = (11 + 1) × 99, = 12 × (100-1), = 12 × 100-12, = 1200-12, = 1188