Question

How to find the dot product of 1×3 vectors
​

Answer 1

The dot product of two 1×3 vectors is calculated by multiplying their corresponding components and summing the results. This yields a scalar that represents the magnitude product and the cosine of the angle between the vectors.

Step-by-step explanation:

The dot product or scalar product of two vectors in three-dimensional space is a number obtained by performing scalar multiplication of corresponding components of the vectors. To calculate the dot product of 1×3 vectors, you follow these steps:

1. Identify the corresponding components of both vectors. Let's consider vectors A and B where A = (a1, a2, a3) and B = (b1, b2, b3).
2. Multiply each corresponding pair of components together. So, you calculate a1*b1, a2*b2, and a3*b3.
3. Add these products together to get the final result: A.B = a1*b1 + a2*b2 + a3*b3.

This value is the dot product of the two vectors. The result is a scalar that represents the product of the vectors' magnitudes and the cosine of the angle between them when equal vectors or when their magnitudes are in a parallel arrangement. If the vectors are orthogonal (at a right angle to each other), their dot product will be zero because the cosine of a 90-degree angle is zero.

Answer 2

Since we know the dot product of unit vectors, we can simplify the dot product formula to a⋅b=a1b1+a2b2+a3b3. we can use the same formula, but with a3=b3=0, a⋅b=a1b1+a2b2.

Step-by-step explanation:

hope it will help u

please mark me brillient