Angle between the vectors - 3 a- b and b- a- b a is

The correct option is A π 2 Let A=√( 3 )( a× b ) and B=b ( a· b ) a A is the vector perpendicular to the plane of a, b . B is t ...

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Standard XII

Mathematics

Applications of Dot Product

Angle between...

Question

Angle between the vectors $\sqrt{3} (a \times b)$ and $b - (a \cdot b) a$ is

\frac{π}{2}

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\frac{π}{4}

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0

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\frac{π}{3}

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Solution

The correct option is A $\frac{π}{2}$
Let $A = \sqrt{3} (a \times b)$ and $B = b - (a \cdot b) a$
$A$ is the vector perpendicular to the plane of $a, b$ .
$B$ is the vector lies in the plane of $a, b$ .
$∴ A \cdot B = 0$
or the angle between them is $\frac{π}{2}$ .

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Angle between the vectors √3(a×b) and b−(a⋅b)a is

The correct option is A π2Let A=√3(a×b) and B=b−(a⋅b)aA is the vector perpendicular to the plane of a,b.B is the vector lies in the plane of a,b.∴A⋅B=0or the angle between them is π2.

Angle between the vectors $\sqrt{3} (a \times b)$ and $b - (a \cdot b) a$ is

The correct option is A $\frac{π}{2}$
Let $A = \sqrt{3} (a \times b)$ and $B = b - (a \cdot b) a$
$A$ is the vector perpendicular to the plane of $a, b$ .
$B$ is the vector lies in the plane of $a, b$ .
$∴ A \cdot B = 0$
or the angle between them is $\frac{π}{2}$ .