# Suppose vector u = <-1, -4,4> and vector v = <1,0,-5> and . What is (vector u cross product vector v) ?

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### 1 Answer

You need to evaluate the cross product of the vectors `bar u` and `bar v` , using the following formula, such that:

`bar u x bar v = [(bar i, bar j, bar k),(u_x,u_y,u_z),(v_x,v_y,v_z)]`

You need to identify `u_x,u_y,u_z` such that:

`u_x = 1,u_y = -4,u_z = 4`

You need to identify `v_x,v_y,v_z` such that:

`v_x = 1,v_y = 0,v_z = -5`

`bar u x bar v = [(bar i, bar j, bar k),(1,-4,4),(1,0,-5)]`

`bar u x bar v = -4*(-5)*bar i + 1*0*bark + 4*1*bar j - 1*(-4)*bar k - 0*4*bar i - 1*(-5)*bar j`

`bar u x bar v = 20 bar i + 9 bar j + 4 bar k`

**Hence, evaluating the cross product of the given vectors, yields **`bar u x bar v = 20 bar i + 9 bar j + 4 bar k.`