Mathematics
Mathematics, 12.09.2019 21:30, louie4052

The scalar product can be described as the magnitude of b times the component of a that is parallel to b. in terms of the positive scalar quantities a, b, and d, what is the component of a that is parallel to b? suppose that c = 0.

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Physics, 22.08.2019 06:30, adam1299
The dot or scalar product of two (3d) vec- tors ⃗a = ⟨a1,a2,a3⟩ and ⃗b = ⟨b1,b2,b3⟩ is defined as 3 ⃗a • ⃗b = a i b i = a 1 b 1 + a 2 b 2 + a 3 b 3 . i=1 in 3d euclidean space, the scalar product has a geometric interpretation, given by ⃗a • ⃗b = ∥ ⃗a ∥ ∥ ⃗b ∥ c o s θ , where θ is the angle between ⃗a and ⃗b and the norm(length) of a vector ∥⃗a∥ is defined by ∥ ⃗a ∥ = √ ⃗a • ⃗a . in words, the scalar product of two vectors can be thought of as the product of the magnitude of ⃗a with the magnitude of the projection of ⃗b onto the direction of ⃗a. it is used to calculate the product of vector quantities when only the parallel components of each vector contribute (e.g., work = force • displacement). let ⃗a = ⟨14, 10.5, 0⟩ and ⃗b = ⟨4.62, 9.45, 0⟩. calculate ⃗a • ⃗b.
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Mathematics, 11.09.2019 00:30, rue61
Vector a⃗ =aiˆ−bkˆ and vector b⃗ =−cjˆ+dkˆ. (a) in terms of the positive scalar quantities a, b, c, and d, what are a⃗ ⋅b⃗ and a⃗ ×b⃗ ? (b) if c=0, what is the magnitude of a⃗ ⋅b⃗ and what are the magnitude and direction of a⃗ ×b⃗ ? does your result for the direction for a⃗ ×b⃗ agree with the result you get if you sketch a⃗ and b⃗ in the xz-plane and apply the right-hand rule? the scalar product can be described as the magnitude of b⃗ times the component of a⃗ that is parallel to b⃗ . does this agree with your result? the magnitude of the vector product can be described as the magnitude of b⃗ times the component of a⃗ that is perpendicular to b⃗ . does this agree with your result?
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Mathematics, 01.10.2019 22:20, Arealbot
Vector a⃗ =aiˆ−bkˆ and vector b⃗ =−cjˆ+dkˆ. (a) in terms of the positive scalar quantities a, b, c, and d, what are a⃗ ⋅b⃗ and a⃗ ×b⃗ ? (b) if c=0, what is the magnitude of a⃗ ⋅b⃗ and what are the magnitude and direction of a⃗ ×b⃗ ? does your result for the direction for a⃗ ×b⃗ agree with the result you get if you sketch a⃗ and b⃗ in the xz-plane and apply the right-hand rule? the scalar product can be described as the magnitude of b⃗ times the component of a⃗ that is parallel to b⃗ . does this agree with your result? the magnitude of the vector product can be described as the magnitude of b⃗ times the component of a⃗ that is perpendicular to b⃗ . does this agree with your result?
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