If 2 i -5 j and 3 i -4 j are 2 vectors in x - y plane then the determinant - 2 5- 3 4 - will give the area of the parallelogram formed by the two vectors in the x - y plane-A- TrueB- False

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Definition of a Determinant

If 2 i +5 j a...

Question

If $2 i + 5 j$ and $3 i + 4 j$ are 2 vectors in $x - y$ plane then the determinant $∣ ∣ ∣ \begin{matrix} 2 & 5 3 & 4 \end{matrix} ∣ ∣ ∣$ will give the area of the parallelogram formed by the two vectors in the $x - y$ plane.

True

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False

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Solution

The correct option is A
True

We have discussed that the 2 vectors in $x - y$ plane can be represented in the form of a matrix. For these two vectors the matrix will be $[\begin{matrix} 2 & 3 3 & 4 \end{matrix}]$ and the determinant of this gives the area of the parallelogram formed by them.

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Similar questions

Q. If

2 i + 5 j

and

3 i + 4 j

are 2 vectors in xy plane then the determinant

∣ ∣ ∣ \begin{matrix} 2 & 5 3 & 4 \end{matrix} ∣ ∣ ∣

will give the area of the formed by the two vectors in the x-y plane.

If $2 i + 5 j$ and $3 i + 4 j$ are 2 vectors in $x - y$ plane then the determinant $∣ ∣ ∣ \begin{matrix} 2 & 5 3 & 4 \end{matrix} ∣ ∣ ∣$ will give the area of the parallelogram formed by the two vectors in the $x - y$ plane.

Q. If

_{1} a n d_{2}

are two vectors in x – y plane. Then any vector in that plane can be obtained by the linear combination of these two vectors.The statement is

Q. The triangle formed by the three points whose position vectors are

2 i + 4 j - k, 4 i + 5 j + k

and

3 i + 6 j - 3 k

, is

Q. The plane which can be formed with the vectors

¯ ¯ ¯ a = 3 ¯ i - 4 ¯ j + 2 ¯ ¯ ¯ k, ¯ ¯ b = 2 ¯ i - ¯ j - 6 ¯ ¯ ¯ k

¯ ¯ c = 5 ¯ i - 5 ¯ j - 4 ¯ ¯ ¯ k

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If 2i+5j and 3i+4j are 2 vectors in x−y plane then the determinant ∣∣∣2534∣∣∣ will give the area of the parallelogram formed by the two vectors in the x−y plane.

The correct option is A True We have discussed that the 2 vectors in x−y plane can be represented in the form of a matrix. For these two vectors the matrix will be[2334]and the determinant of this gives the area of the parallelogram formed by them.

If $2 i + 5 j$ and $3 i + 4 j$ are 2 vectors in $x - y$ plane then the determinant $∣ ∣ ∣ \begin{matrix} 2 & 5 3 & 4 \end{matrix} ∣ ∣ ∣$ will give the area of the parallelogram formed by the two vectors in the $x - y$ plane.

The correct option is A
True

We have discussed that the 2 vectors in $x - y$ plane can be represented in the form of a matrix. For these two vectors the matrix will be $[\begin{matrix} 2 & 3 3 & 4 \end{matrix}]$ and the determinant of this gives the area of the parallelogram formed by them.