If the angle between the vectors $\vec{A} and \vec{B} is θ$ , the value of the product $(\vec{B} \times \vec{A}) . \vec{A}$ is equal to

${BA}^{2} cosθ$

BA² sinθ

BA² sinθ cosθ

zero

Solution

zero

$(\vec{B} \times \vec{A}) . \vec{A} \Rightarrow (\vec{B} \times \vec{A}) . \vec{A} = B A cosθ \hat{n} . \vec{A} = 0$

Here $\hat{n}$ is perpendicular to both $\vec{A} and \vec{B}$ .

Alternative method

$(\vec{B} \times \vec{A}) . \vec{A}$

Interchange the cross and dot we have,

$(\vec{B} \times \vec{A}) . \vec{A} = \vec{B} . (\vec{A} \times \vec{A}) = 0 . . . . . (\vec{A} \times \vec{A} = 0)$

The volume of a parallelopiped bounded by vectors $\vec{A}, \vec{A} and \vec{A}$ can be obtained by giving formula $(\vec{A} \times \vec{A}) . \vec{A}$

Some More Questions From System of Particles and Rotational Motion Chapter

Four point masses, each of value m, are placed at the corners of a square ABCD of side A. The moment of inertia through A and parallel to BD is

A wire elongates by

A ‘T’ shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C

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System Of Particles And Rotational Motion

If the angle between the vectors $\vec{A} and \vec{B} is θ$ , the value of the product $(\vec{B} \times \vec{A}) . \vec{A}$ is equal to

${BA}^{2} cosθ$

BA² sinθ

BA² sinθ cosθ

zero

Some More Questions From System of Particles and Rotational Motion Chapter

Four point masses, each of value m, are placed at the corners of a square ABCD of side A. The moment of inertia through A and parallel to BD is

A wire elongates by

A ‘T’ shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C

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For Daily Free Study Material Join wiredfaculty

System Of Particles And Rotational Motion

If the angle between the vectors A→ and B→ is θ, the value of the product B→ × A→. A→ is equal to BA2 cosθ BA2 sinθ BA2 sinθ cosθ zero

Some More Questions From System of Particles and Rotational Motion Chapter

Four point masses, each of value m, are placed at the corners of a square ABCD of side A. The moment of inertia through A and parallel to BD is

A wire elongates by

A ‘T’ shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If the angle between the vectors $\vec{A} and \vec{B} is θ$ , the value of the product $(\vec{B} \times \vec{A}) . \vec{A}$ is equal to

${BA}^{2} cosθ$

BA² sinθ

BA² sinθ cosθ

zero