Calculate the cross product assuming that u × w = 0, 1, 3 . (2u + 3w) × w

Answer- (2u + 3w) × w =  < 0, 2, 6 >

Solution -

Given in the problem

(u × w) = < 0, 1, 3 >

Then,

(2u + 3w) × w = (2u × w) + (3w × w)

(2u × w) = 2(u × w) = < 0×2, 1×2, 3×2 > = < 0, 2, 6 >  ( ∵ Multiplying it by 3 with all components)

(3w × w) = 3(w × w) = 0                                               ( ∵ The cross product of any vector with itself is 0)

∴ (2u + 3w) × w =  < 0, 2, 6 >

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

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