Question

For \(\vec{A} = x \hat{a}_x + y \hat{a}_y + z \hat{a}_z\) and \(\vec{B} = 3x \hat{a}_x + 2y \hat{a}_y + 4z \hat{a}_z\) Find the following a) \(\vec{C} = \vec{A} \times \vec{B}\) b) at \((1, 2, 3)\) find \(|\vec{A} \times \vec{B}|\), angle \(\theta\) between \(\vec{A}\) and \(\vec{B}\), and \(\hat{a}_n\) c) \(D = \vec{A}.\vec{B}\) at \((1, 2, 3)\)

          For \(\vec{A} = x \hat{a}_x + y \hat{a}_y + z \hat{a}_z\) and \(\vec{B} = 3x \hat{a}_x + 2y \hat{a}_y + 4z \hat{a}_z\)
Find the following
a) \(\vec{C} = \vec{A} \times \vec{B}\)
b) at \((1, 2, 3)\) find \(|\vec{A} \times \vec{B}|\), angle \(\theta\) between \(\vec{A}\) and \(\vec{B}\), and \(\hat{a}_n\)
c) \(D = \vec{A}.\vec{B}\) at \((1, 2, 3)\)

For A⃗ = x âx + y ây + z âz and B⃗ = 3x âx + 2y ây + 4z âz
Find the following
a) C⃗ = A⃗×B⃗
b) at (1, 2, 3) find |A⃗×B⃗|, angle θ between A⃗ and B⃗, and ân
c) D = A⃗.B⃗ at (1, 2, 3)

Added by Matthew D.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Mahendra Kumar

Step 1

To find the cross product C = A x B, we can use the formula for the cross product: C = (AyBz - AzBy)ax + (AzBx - AxBz)ay + (AxBy - AyBx)az Plugging in the values from A and B: C = ((ya * 4za) - (za * 2ya))ax + ((za * 3xa) - (xa * 4za))ay + ((xa * 2ya) - (ya * Show more…

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For A = xax + yay + zaz and B = 3xax + 2yay + 4zaz, find the following: a) C = A x B b) Find A x B | angle Î¸ between A and B, and an c) D = A Â· B at (1,2,3)