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Given that A + B = R and A² + B² = R². The angle between A and B is

Consider two vectors \(\hat{F}_{1}=2\hat{i}+5\hat{k}\) and \(\hat{F}_{2}=3\hat{j}+4\hat{k}\) The magnitude of the scalar product of these vectors is

Solution

\(\dot{F}_{1}.\dot{F}_{2}=(2\hat{i}+5\hat{k})\cdot (3\hat{j}+4\hat{k})=20\)

If \(\hat{n}\) is a unit vector in the direction of the vector A, then

Solution

The unit vector of any vector \(\dot{A}\)is defined as

\(\hat{A}=\frac{\dot{A}}{\left | \dot{A} \right |}\)

Three vectors A, B and C satisfy the relation A B = 0 and A C = 0. The vector A is parallel to

Solution

Since \(\dot{A}.\dot{C}=0=\dot{A}.\dot{B}\), it means that \(\dot{A}\)
is perpendicular to both \(\dot{C}\: and\: \dot{B}\), hence \(\dot{A}\)
is parallel to \((\dot{B}\times \dot{C})\)or\((\dot{C}\times \dot{B})\).

If A and B are two vectors, then the correct statement is

Solution

In vector addition, the commutative law is obeyed

\(\frac{i.e.,\dot{A}+\dot{B}=\dot{B}+\dot{A}}{Vector\: subtraction\: does\: not\: follow\: commutative\: law.}\)

The greatest height to which a man can through a ball is h.What is the greatest horizontal distance to which he can throw the ball?

Which of the following is not correct ?

The angular speed of a fly-wheel making 120 revolutions/minute is

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