Question

if a bar and B bar are two vectors of finite magnitude then the component of a bar​

Answer 1

Answer:

Answer:

{\underline{\underline{\maltese\textbf{\textsf{\red{Question}}}}}}✠Question

: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bigg({8 - \dfrac{2x}{3}} \bigg)}:⟹(2x−6)=(8−32x)

\begin{gathered}\end{gathered}

{\underline{\underline{\maltese\textbf{\textsf{\red{Solution}}}}}}✠Solution

: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{2x}{3}} \bigg)}:⟹(2x−6)=(8−32x)

{: \implies{\sf\bigg({\dfrac{x - (6 \times 2)}{2}}\bigg) = \bf\bigg({\dfrac{(8 \times 3) - 2x}{3}} \bigg)}}:⟹(2x−(6×2))=(3(8×3)−2x)

{: \implies{\sf\bigg({\dfrac{x - 12}{2}}\bigg) = \bf\bigg({\dfrac{24 - 2x}{3}} \bigg)}}:⟹(2x−12)=(324−2x)

By cross multiplication

: \implies\sf{3(x - 12) = \bf{2(24 - 2x)}}:⟹3(x−12)=2(24−2x)

: \implies\sf{3x - 36 = \bf{48 - 4x}}:⟹3x−36=48−4x

: \implies\sf{4x - 3x = \bf{48 -36}}:⟹4x−3x=48−36

: \implies\sf{x = \bf{12}}:⟹x=12

{\dag{\underline{\boxed{\sf{x =12}}}}}†x=12

Hence, The value of x is 12.

\begin{gathered}\end{gathered}

{{\underline{\underline{\maltese\textbf{\textsf{\red{Verification}}}}}}}✠Verification

: \implies{\sf\bigg({\dfrac{x}{2} - 6}\bigg) = \bf\bigg({8 - \dfrac{2x}{3}} \bigg)}:⟹(2x−6)=(8−32x)

Substituting the value of

Answer 2

Answer:

Component of A in the direction of B = (A . B) / ||B|| * B

Explanation:

From the above question,

They have given :

If two vectors A and B are of finite magnitude, the component of vector A in the direction of vector B can be found using the following formula:

Component of A in the direction of B = (A . B) / ||B|| * B

Where A . B represents the dot product of vectors A and B, and ||B|| represents the magnitude of vector B. The dot product of two vectors gives the projection of one vector onto another, and the magnitude of the resulting vector is equal to the magnitude of the projection.

In this formula,

            The dot product of vectors A and B is divided by the magnitude of vector B to give the magnitude of the projection, and this result is then multiplied by vector B to give the projection vector in the direction of B. The projection vector represents the component of vector A in the direction of vector B.

It's important to note that the component of a vector in a certain direction is a scalar value that represents the magnitude of the projection of the vector onto that direction, and the projection vector itself represents the direction and magnitude of that projection.

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