The vector product of [tex]\boxed{a \times b = - 43\hat k}[/tex] and the magnitude of [tex]a \times b[/tex] is [tex]\boxed{43}.[/tex]
Further explanation:
Given:
Vector a is [tex]\vec a = 4.00\hat i + 7.00\hat j.[/tex]
Vector b is [tex]\vec b = 5.00\hat i - 2.00\hat j.[/tex]
Explanation:
The cross product of a \times b can be obtained as follows,
[tex]\begin{aligned}a \times b &= \left| {\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k} \\4&7&0\\5&{ - 2}&0 \end{array}}\right|\\&= \hat i\left( {0 - 0} \right) - \hat j\left( {0 - 0} \right) + \hat k\left( { - 9 - 35} \right)\\&= 0\hat i - 0\hat j - 43\hat k\\&= - 43\hat k\\\end{aligned}[/tex]
The vector can be expressed as follows,
[tex]a \times b = - 43\hat k[/tex]
The magnitude of [tex]a \times b[/tex]can be obtained as follows,
[tex]\begin{aligned}\left| {a \times b} \right| &= \sqrt {{0^2} + {0^2} + {{\left( { - 43} \right)}^2}}\\&= \sqrt {{{43}^2}}\\&= 43\\\end{aligned}[/tex]43404
The vector product of [tex]\boxed{a \times b = - 43\hat k}[/tex] and the magnitude of [tex]a \times b[/tex] is [tex]\boxed{43}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Vectors
Keywords: two vectors, vector product, expressed in unit vectors, magnitude, vector a, vector b, a=4.00i^+7.00j^, b=5.00i^-2.00j^, unit vectors, vector space.
