Question

If the angle between a vector and b vector is π/3 ,then angle between 2a vector and -3b vector is :

Answer 1

Answer:

Explanation:

Given, the angle between A and B = $\pi/3$ = 60 degrees.

Now, multiplying any vector with scalar quantity doesn't affect its direction.(assuming the scalar to be positive)

But, as there is negative sign before 3B, its direction will be reversed.

Thus the angle between 2A and -3B will be 60+180= 240 degrees

                                                                                =$4\pi /3$ (Ans.)

Answer 2

Answer:

If the angle between a vector and b vector is π/3, then the angle between 2a vector and -3b vector is 2π/3.

Explanation:

• Draw vectors $a$ and $b$ (Refer figure no.1).
• Draw vectors $2a$ and $-3b$ (Refer figure no.2).
• Vector $2a$ will be twice the length of the vector $a$ in the same direction.
• Vector $-3b$ will be thrice the size of vector $b$ but in opposite direction.

Let Φ be the angle between $2a$ and $-3b$ .

Φ = $\pi -\frac{\pi }{3}$

Ф = $\frac{2\pi }{3}$

As a result, the angle formed by the vectors $2a$ and $-3b$ is $\frac{2\pi }{3}$.

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