The value of the expression
Answer to Problem 18E
The value of the expression
Explanation of Solution
Given information:
The value of the vectors in component form
Formula used:
If there are two three-dimensional vectors in a space given in the form of their components, say,
Any two non-zero vectors are said to be orthogonal to each other if and only if their dot product is zero, i.e. the angle between the two vectors is
Calculation:
Consider the given value of the vectors
Recall that ifthere are two three-dimensional vectors in a space given in the form of their components, say,
Apply it,
So, the cross product of u and v vectors will be calculated as,
Simplify it further as,
Now, recall that any two non-zero vectors are said to be orthogonal to each other if and only if their dot product is zero, i.e. the angle between the two vectors is
So, to prove that the product obtained is orthogonal to both u and v, we will calculate the dot product of u and v with
So, the dot product of u and
Since, dot product of u and
Now, dot product of v and
Since, dot product of v and
Hence, the value of the expression
Chapter 11 Solutions
EBK PRECALCULUS W/LIMITS
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