Figure shows four vectors A? , B?? , C? , and D?? with magnitude A = 4, B = 3, C = 7 and D = 9. Find out the angle between the vectors 2????A?? × B?? and (A? ? C?) × (B?? + D??)
Added by Roshir P.
Step 1
First, we need to find the cross products of the given vectors: Show more…
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Two vectors are given by $\overrightarrow{\mathbf{A}}=-3 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ and $\overrightarrow{\mathbf{B}}=$ $6 \hat{\mathbf{i}}-10 \hat{\mathbf{j}}+9 \hat{\mathbf{k}} .$ Evaluate the quantities (a) $\cos ^{-1}[\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}} / A B]$ and (b) $\sin ^{-1}[|\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}| / A B]$ (c) Which give(s) the angle between the vectors?
For the vectors $\mathbf{A}=-3 \mathbf{i}+7 \mathbf{j}-4 \mathbf{k}$ and $\mathbf{B}=6 \mathbf{i}-10 \mathbf{j}+$ $9 \mathbf{k}$, evaluate the expressions (a) $\cos ^{-1}(\mathbf{A} \cdot \mathbf{B} / A B)$ and (b) $\sin ^{-1}(|\mathbf{A} \times \mathbf{B}| / A B) \cdot$ (c) Which give(s) the angle between the vectors?
Two vectors are given by $\overrightarrow{\mathbf{A}}=-3 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ and $\overrightarrow{\mathbf{B}}=6 \hat{\mathbf{i}}-10 \hat{\mathbf{j}}+9 \hat{\mathbf{k}} .$ Evaluate the quantities (a) $\cos ^{-1}[\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}} / A B]$ and (b) $\sin ^{-1}[|\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}| / A B] .$ (c) Which give(s) the angle between the vectors?
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