Advertisements
Advertisements
प्रश्न
Classify the following measures as scalar and vector.
10 kg
Advertisements
उत्तर
10 kg is a scalar quantity because it involves only magnitude.
APPEARS IN
संबंधित प्रश्न
If `bara, barb, bar c` are the position vectors of the points A, B, C respectively and ` 2bara + 3barb - 5barc = 0` , then find the ratio in which the point C divides line segment AB.
Find the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector
`2hati+3hatj+4hatk` to the plane `vecr` . `(2hati+hatj+3hatk)−26=0` . Also find image of P in the plane.
Find the value of 'p' for which the vectors `3hati+2hatj+9hatk and hati-2phatj+3hatk` are parallel
If `bara, barb, barc` are position vectors of the points A, B, C respectively such that `3bara+ 5barb-8barc = 0`, find the ratio in which A divides BC.
Classify the following as scalar and vector quantity.
Time period
`veca and -veca` are collinear.
Two vectors having the same magnitude are collinear.
Find the direction cosines of the vector `hati + 2hatj + 3hatk`.
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are `hati + 2hatj - hatk` and `-hati + hatj + hatk` respectively, externally in the ratio 2:1.
Show that the points A, B and C with position vectors `veca = 3hati - 4hatj - 4hatk`, `vecb = 2hati - hatj + hatk` and `vecc = hati - 3hatj - 5hatk`, respectively form the vertices of a right angled triangle.
Find the value of x for which `x(hati + hatj + hatk)` is a unit vector.
Express \[\vec{AB}\] in terms of unit vectors \[\hat{i}\] and \[\hat{j}\], when the points are A (4, −1), B (1, 3)
Find \[\left| \vec{A} B \right|\] in each case.
Express \[\vec{AB}\] in terms of unit vectors \[\hat{i}\] and \[\hat{j}\], when the points are A (−6, 3), B (−2, −5)
Find \[\left| \vec{A} B \right|\] in each case.
Find the angle between the vectors \[\vec{a} \text{ and } \vec{b}\] where \[\vec{a} = \hat{i} - \hat{j} \text{ and } \vec{b} = \hat{j} + \hat{k}\]
Find the angle between the vectors \[\vec{a} \text{ and } \vec{b}\] \[\vec{a} = 2\hat{i} - \hat{j} + 2\hat{k} \text{ and } \vec{b} = 4\hat{i} + 4 \hat{j} - 2\hat{k}\]
Find the angle between the vectors \[\vec{a} = 2 \hat{i} - 3 \hat{j} + \hat{k} \text{ and } \vec{b} = \hat{i} + \hat{j} - 2 \hat{k}\]
Find the angle between the vectors \[\vec{a} = \hat{i} + 2 \hat{j} - \hat{k} , \vec{b} = \hat{i} - \hat{j} + \hat{k}\]
Find the angles which the vector \[\vec{a} = \hat{i} -\hat {j} + \sqrt{2} \hat{k}\] makes with the coordinate axes.
Dot products of a vector with vectors \[\hat{i} - \hat{j} + \hat{k} , 2\hat{ i} + \hat{j} - 3\hat{k} \text{ and } \text{i} + \hat{j} + \hat{k}\] are respectively 4, 0 and 2. Find the vector.
For any two vectors \[\vec{a} \text{ and } \vec{b}\] show that \[\left( \vec{a} + \vec{b} \right) \cdot \left( \vec{a} - \vec{b} \right) = 0 \Leftrightarrow \left| \vec{a} \right| = \left| \vec{b} \right|\]
If \[\vec{p} = 5 \hat{i} + \lambda \hat{j} - 3 \hat{k} \text{ and } \vec{q} = \hat{i} + 3 \hat{j} - 5 \hat{k} ,\] then find the value of λ, so that \[\vec{p} + \vec{q}\] and \[\vec{p} - \vec{q}\] are perpendicular vectors.
If \[\vec{a} = 2 \hat{i} + 2 \hat{j} + 3 \hat{k} , \vec{b} = - \hat{i} + 2 \hat{j} + \hat{k} \text{ and } \vec{c} = 3 \hat{i} + \hat{j}\] \[\vec{a} + \lambda \vec{b}\] is perpendicular to \[\vec{c}\] then find the value of λ.
Show that the points whose position vectors are \[\vec{a} = 4 \hat{i} - 3 \hat{j} + \hat{k} , \vec{b} = 2 \hat{i} - 4 \hat{j} + 5 \hat{k} , \vec{c} = \hat{i} - \hat{j}\] form a right triangle.
Find the unit vector in the direction of vector \[\overrightarrow{PQ} ,\]
where P and Q are the points (1, 2, 3) and (4, 5, 6).
If \[\overrightarrow{AO} + \overrightarrow{OB} = \overrightarrow{BO} + \overrightarrow{OC} ,\] prove that A, B, C are collinear points.
Show that the vectors \[2 \hat{i} - 3 \hat{j} + 4 \hat{k}\text{ and }- 4 \hat{i} + 6 \hat{j} - 8 \hat{k}\] are collinear.
If \[\vec{a} \times \vec{b} = \vec{c} \times \vec{d} \text { and } \vec{a} \times \vec{c} = \vec{b} \times \vec{d}\] , show that \[\vec{a} - \vec{d}\] is parallel to \[\vec{b} - \vec{c}\] where \[\vec{a} \neq \vec{d} \text { and } \vec{b} \neq \vec{c}\] .
If `vec"a"` and `vec"b"` are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.
A vector `vec"r"` has magnitude 14 and direction ratios 2, 3, – 6. Find the direction cosines and components of `vec"r"`, given that `vec"r"` makes an acute angle with x-axis.
The unit normal to the plane 2x + y + 2z = 6 can be expressed in the vector form as
If `veca, vecb, vecc` are vectors such that `[veca, vecb, vecc]` = 4, then `[veca xx vecb, vecb xx vecc, vecc xx veca]` =
Area of rectangle having vertices A, B, C and D will position vector `(- hati + 1/2hatj + 4hatk), (hati + 1/2hatj + 4hatk) (hati - 1/2hatj + 4hatk)` and `(-hati - 1/2hatj + 4hatk)` is
If points A, B and C have position vectors `2hati, hatj` and `2hatk` respectively, then show that ΔABC is an isosceles triangle.
