If 2i -5j and 3i-4j are 2 vectors in x-y plane then the determinant 2 53 4 will give the area of the parallelogram formed by the two vectors in the x-y plane-

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Definition of a Determinant

If 2i +5j and...

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

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

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.

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

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. A vector

C

when added to vectors

A = 3 ˆ i - 5 ˆ j + ˆ k

and

B = 2 ˆ i + 3 ˆ j - 4 ˆ k

gives a unit vector along the y-axis. Then,

C

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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.