The magnitude of vectors \(\vec{A},\vec{B}\) and \(\vec{C}\) are 3, 4 and 5 units respectively. If \(\vec{A} + \vec{B} = \vec{C}\) , the angle between \(\vec{A}\) and \(\vec{B}\) is:
(1988)
1. \(\pi/2\)
2. \(cos^{-1} (0.6)\)
3. \(tan^{-1} (7/5)\)
4. \(\pi/4\)
View Answer
Given \(|\vec{A}|=3, |\vec{B}|=4, |\vec{C}|=5\) and \(\vec{A} + \vec{B} = \vec{C}\). Squaring both sides: \(|\vec{A} + \vec{B}|^2 = |\vec{C}|^2\). \(|\vec{A}|^2 + |\vec{B}|^2 + 2|\vec{A}||\vec{B}|cos\theta = |\vec{C}|^2\). Substituting values: \(3^2 + 4^2 + 2(3)(4)cos\theta = 5^2\) which gives \(9 + 16 + 24cos\theta = 25\). Thus, \(24cos\theta = 0\) and \(\theta = \pi/2\).
Given below are two statements one is labelled as assertion (A) and reason (R)
Assertion: The length of actual path travelled by a body in given time interval is always equal to displacement.
Reason: If displacement is zero, then body is either at rest or it has returned to initial position.
Choose the correct option.
1. Assertion is true but Reason is false
2. Assertion is false but Reason is true
3. Both Assertion and Reason are true and Reason is correct explanation of Assertion
4. Both Assertion and Reason are true and Reason is not the correct explanation of Assertion
View Answer
Distance (actual path length) is greater than or equal to displacement magnitude, so the assertion is false. If displacement is zero, the body either remained at rest or returned to its starting point, making the reason true.