Advertisements
Advertisements
प्रश्न
Classify the following as scalars and vector quantities:
(i) Time period
(ii) Distance
(iii) displacement
(iv) Force
(v) Work
(vi) Velocity
(vii) Acceleration
उत्तर
The quantities which have only magnitude and which are not related to any
fixed direction in space are called scaler quantities or simply scalars.
The quantities which have both magnitude and direction are called vector quantities or simply vectors.
(i) Scalar
(ii) Scalar
(iii) Vector
(iv)Vector
(v) Scalar
(vi) Vector
(vii) Vector
APPEARS IN
संबंधित प्रश्न
Classify the following measures as scalars and vectors:
(i) 15 kg
(ii) 20 kg weight
(iii) 45°
(iv) 10 meters south-east
(v) 50 m/sec2
Answer the following as true or false:
\[\vec{a}\] and \[\vec{a}\] are collinear.
Answer the following as true or false:
Two collinear vectors are always equal in magnitude.
Answer the following as true or false:
Zero vector is unique.
Answer the following as true or false:
Two collinear vectors having the same magnitude are equal.
If \[\vec{a}\] and \[\vec{b}\] are two non-collinear vectors having the same initial point. What are the vectors represented by \[\vec{a}\] + \[\vec{b}\] and \[\vec{a}\] − \[\vec{b}\].
If \[\vec{a}\] is a vector and m is a scalar such that m \[\vec{a}\] = \[\vec{0}\], then what are the alternatives for m and \[\vec{a}\] ?
Five forces \[\overrightarrow{AB,} \overrightarrow { AC,} \overrightarrow{ AD,}\overrightarrow{AE}\] and \[\overrightarrow{AF}\] act at the vertex of a regular hexagon ABCDEF. Prove that the resultant is 6 \[\overrightarrow{AO,}\] where O is the centre of hexagon.
Show that the points A (1, −2, −8), B (5, 0, −2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.
If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are non-zero, non-coplanar vectors, prove that the following vectors are coplanar:
(1) \[5 \vec{a} + 6 \vec{b} + 7 \vec{c,} 7 \vec{a} - 8 \vec{b} + 9 \vec{c}\text{ and }3 \vec{a} + 20 \vec{b} + 5 \vec{c}\]
Prove that the following vectors are coplanar:
\[\hat{i} + \hat{j} + \hat{k} , 2 \hat{i} + 3 \hat{j} - \hat{k}\text{ and }- \hat{i} - 2 \hat{j} + 2 \hat{k}\]
If \[\vec{a}\], \[\vec{a}\], \[\vec{c}\] are non-coplanar vectors, prove that the following vectors are non-coplanar: \[2 \vec{a} - \vec{b} + 3 \vec{c} , \vec{a} + \vec{b} - 2 \vec{c}\text{ and }\vec{a} + \vec{b} - 3 \vec{c}\]
Show that the vectors \[\vec{a,} \vec{b,} \vec{c}\] given by \[\vec{a} = \hat{i} + 2 \hat{j} + 3 \hat{k} , \vec{b} = 2 \hat{i} + \hat{j} + 3 \hat{k}\text{ and }\vec{c} = \hat{i} + \hat{j} + \hat{k}\] are non coplanar.
Express vector \[\vec{d} = 2 \hat{i}-j- 3 \hat{k} , \text{ and }\text { as a linear combination of the vectors } \vec{a,} \vec{b}\text{ and }\vec{c} .\]
The vector (cos α cos β) \[\hat{i}\] + (cos α sin β) \[\hat{j}\] + (sin α) \[\hat{k}\] is a
If the position vectors of P and Q are \[\hat{i} + 3 \hat{j} - 7 \hat{k} \text{ and } 5 \text{i} - 2 \hat{j} + 4 \hat{k}\] then the cosine of the angle between \[\vec{PQ}\] and y-axis is
If the vectors `hati - 2xhatj + 3 yhatk and hati + 2xhatj - 3yhatk` are perpendicular, then the locus of (x, y) is ______.
The vector component of \[\vec{b}\] perpendicular to \[\vec{a}\] is
What is the length of the longer diagonal of the parallelogram constructed on \[5 \vec{a} + 2 \vec{b} \text{ and } \vec{a} - 3 \vec{b}\] if it is given that \[\left| \vec{a} \right| = 2\sqrt{2}, \left| \vec{b} \right| = 3\] and the angle between \[\vec{a} \text{ and } \vec{b}\] is π/4?
If \[\vec{a} , \vec{b} , \vec{c}\] are any three mutually perpendicular vectors of equal magnitude a, then \[\left| \vec{a} + \vec{b} + \vec{c} \right|\] is equal to
The projection of the vector \[\hat{i} + \hat{j} + \hat{k}\] along the vector of \[\hat{j}\] is
The vectors \[2 \hat{i} + 3 \hat{j} - 4 \hat{k}\] and \[a \hat{i} + \hat{b} j + c \hat{k}\] are perpendicular if
If \[\left| \vec{a} \right| = \left| \vec{b} \right|, \text{ then } \left( \vec{a} + \vec{b} \right) \cdot \left( \vec{a} - \vec{b} \right) =\]
If \[\vec{a} \text{ and } \vec{b}\] are unit vectors, then the greatest value of \[\sqrt{3}\left| \vec{a} + \vec{b} \right| + \left| \vec{a} - \vec{b} \right|\]
If the angle between the vectors \[x \hat{i} + 3 \hat{j}- 7 \hat{k} \text{ and } x \hat{i} - x \hat{j} + 4 \hat{k}\] is acute, then x lies in the interval
If \[\vec{a} \text{ and } \vec{b}\] are two unit vectors inclined at an angle θ, such that \[\left| \vec{a} + \vec{b} \right| < 1,\] then
Let \[\vec{a} , \vec{b} , \vec{c}\] be three unit vectors, such that \[\left| \vec{a} + \vec{b} + \vec{c} \right|\] =1 and \[\vec{a}\] is perpendicular to \[\vec{b}\] If \[\vec{c}\] makes angles α and β with \[\vec{a} and \vec{b}\] respectively, then cos α + cos β =
The orthogonal projection of \[\vec{a} \text{ on } \vec{b}\] is
If \[\vec{a} \text{ and }\vec{b}\] be two unit vectors and θ the angle between them, then \[\vec{a} + \vec{b}\] is a unit vector if θ =
