Question 196: Motion in 2D & Vectors

Question

If the angle  between the vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ is $$	heta $$, the value of the product $$\left( {\overrightarrow B  	imes \overrightarrow A } ight).\overrightarrow A $$ is equal to

Accepted Answer

Let $$\overrightarrow A  	imes \overrightarrow B  = \overrightarrow C $$
The cross product of $$\overrightarrow B $$ and $$\overrightarrow A $$ is perpendicular
to the plane containing $$\overrightarrow A $$
and $$\overrightarrow B $$
i.e. perpendicular
to $$\overrightarrow B $$
If a dot product of this cross product and $$\overrightarrow A $$ is taken, as
the cross product is perpendicular to $$\overrightarrow A $$, $$\overrightarrow C $$ $$ 	imes $$ $$\overrightarrow A $$ = 0
Therefore product of $$\left( {\overrightarrow A  	imes \overrightarrow B } ight) 	imes \overrightarrow A  = 0$$

Answer

BA2sin$$	heta $$

Answer

BA2cos$$	heta $$

Answer

BA2sin$$	heta $$cos$$	heta $$

Answer

zero.

Motion in 2D & Vectors

If the angle between the vectors $\overrightarrow A and \overrightarrow B is \theta , the value of the product \left( {\overrightarrow B \times \overrightarrow A } \right).\overrightarrow A $ is equal to

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