问题1.用图形表示以下内容：
(i)位移40 km，30° 北部以东
(ii)东南方50公里的排水量
(iii)位移70公里，向西40度。
解决方案：
(i) The vector OQ represents the displacement of 40 km, 30° east of north
(ii) The vector OR represents the displacement of 50 km, south-east
(iii) The vector OQ represents the displacement of 70 km, 40° north of west.
问题2 。将以下度量分类为标量和向量：
(i)15公斤(ii)20公斤重量(iii)45°(iv)东南10米(v)50 m / sec 2
解决方案：
Note: Scalar quantities have only magnitude and are not related to any fixed direction in space. Vector quantities have both magnitude and direction
(i) 15 kg involves only mass – Scalar
(ii) 20 kg weight kg involves both magnitude and direction – Vector
(iii) 45° involves only magnitude – Scalar
(iv) 10 meters south-east involves direction – Vector
(v) 50 m/sec 2 involves magnitude of acceleration – Scalar
问题3 。将以下度量分类为标量和向量：
(i)时间段(ii)距离(iii)位移(iv)力(v)功(vi)速度(vii)加速度
解决方案：
Note: Scalar quantities have only magnitude and are not related to any fixed direction in space. Vector quantities have both magnitude and direction
(i) Time period involves only magnitude – Scalar
(ii) Distance involves only magnitude – Scalar
(iii) Displacement involves both magnitude and direction – Vector
(iv) Force involves both magnitude and direction- Vector
(v) Work done involves only magnitude – Scalar
(vi) Velocity involves both magnitude and direction – Vector
(vii) Acceleration involves both magnitude and direction – Vector
问题4。在图中，ABCD是一个正六边形，其向量为：
(i)共线(ii)相等(iii)初始(iv)共线但不相等
解决方案：
In the given figure Vectors:
(i) a, d ;
b, x, z ;
c,y
are Collinear vectors as they have same or parallel supports
(ii) b, x ;
a, d ;
c, y
are equal vectors as they have same length, the same or parallel support and, the same sense
(iii) a, y, z
are Co-initial Vectors having same initial point
(iv) b, z ;
x, z
are Collinear Vectors but not equal as they are parallel, but their lengths are not the same.
问题5.回答以下是对还是错：
(i)a和b向量是共线的
(ii)两个共线向量的大小始终相等
(iii)零向量是唯一的。
(iv)具有相同大小的两个向量是共线的
(v)具有相同大小的两个共线向量相等
Answer 5.
(i) True. As vectors having same or parallel supports are Collinear
(ii) False. Two Collinear vectors must have same supports and may not be equal in magnitude
(iii) False. Zero vector may not be unique
(iv) False. Two vectors having same magnitude may not be collinear
(v) False. Two collinear vectors having same magnitude may not be equal