If θ is the angle between two vectors and , then only when (A) (B) (C) (D)

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Solution

Consider that the angle between the two vectors a → and b → is θ.

The formula for dot product of vectors a → and b → is,

a → ⋅ b → =| a → || b → |cosθ

Assume | a → |≠0 and | b → |≠0.

It is given that,

a → ⋅ b → ≥0 | a → || b → |cosθ≥0 cosθ≥ 0 | a → || b → | cosθ≥0

It is known that, cosθ≥0when 0≤θ≤ π 2 .

Thus, option (B) is correct.

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Choose the correct answer
If $θ$ is the angle between two vectors a and b, then $a . b \geq 0$ only when
a) $0 < θ < \frac{π}{2}$
b) $0 \leq θ < \frac{π}{2}$
c) $0 < θ < π$
d) $0 \leq θ \leq π$

Q. If θ is the angle between two vectors

\vec{a} and \vec{b}, then \vec{a} \cdot \vec{b} \geq 0

only when
(a)

0 < θ < \frac{π}{2}

(b)

0 \leq θ \leq \frac{π}{2}

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