Using the definition of the scalar product, find the angle between the following vectors. (Find the smallest nonnegative angle.) (a) A = 7i − 8j and B = 3i − 5j °
(b) A = −3i + 6j and B = 3i − 4j + 2k °
a) definition of scalar product :
A .B = |A| |B| cos@
(7i - 8j) . ( 3i - 5j) = ( sqrt(7^2 + 8^2 ) sqrt(3^2 + 5^2) )
cos@
61 = ( 10.63 ) ( 5.83) cos@
cos@ =0.984
@ = 10.17 deg
b)
A .B = |A| |B| cos@
(-3i + 6j) . ( 3i - 4j + 2k) = ( sqrt(3^2 + 6^2 ) sqrt(3^2 + 4^2 +
2^2) ) cos@
-33 = (6.71) (5.39) cos@
@ = 155.96 deg
Using the definition of the scalar product, find the angle between the following vectors. (Find the...
Using the definition of the scalar product, find the angle between the following vectors. (Find the smallest nonnegative angle.) (a) A = 6i - 7j and B = 8i - 5j [17.33] (b) A = 3i + 3j and B = 3i - 4j + 2k (c) A = i - 2j + 2k and B = 3j + 4k
4. Determine the scalar triple product of the vectors: 3i2k and c = 3i+ j + 2k a i2jk; b 5. Ifa 3i 2j - k; b = 2i +5j - kand C i + 2j - 2k, find: ax (b x c) (ax b) x t i. ii
4. Determine the scalar triple product of the vectors: 3i2k and c = 3i+ j + 2k a i2jk; b 5. Ifa 3i 2j - k; b = 2i +5j -...
6.
2D vectors
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? &Define a unit vector. Give an example of a...
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ture Supplement 4: Intro Vectors Worksheet B a vector (graphical, verbal, or mathematical) that is in: Provide an example of a) ID b) 2D c) 3D (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? 3,Define a unit vector. Give an example of a unit vector in...
7.
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? &Define a unit vector. Give an example of a unit vector...
Test 1 Version B Two vectors are given by A -3i + 5j-2k and B 4i + 6j +7k (a) Find A B (b) What is the angle between the vectors?
5. Find the i) scalar and ii) vector projections of v onto u if u = 7i+j – 2k and v= 3i -5j +2k
Two vectors A = -3i + 4j - 2k and B = 5j + 2k act on an object. Determine: (a) the magnitude of A the magnitude of B A: B the angle between A and B
8. Given the vectors: A 3i -4j & Bi+ 6j, a) Graph vector A & vector B on the same coordinate system b) Find the scalar product A.B c) Find the magnitude of vector A d) Find the magnitude of vector B- e) Find the angle between vector A & vector B
If a = 2i + 4j and b = 6j-4k get the smallest angle between the two vectors by using: (a) Cross Product (b) Dot Product