The two adjacent sides of a parallelogram areand .
Find the unit vector parallel to its diagonal. Also, find its area.
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If θ is the angle between any two vectors and, then when θisequal to
(A) 0 (B) (C) (D) π
The value of is
(A) 0 (B) –1 (C) 1 (D) 3
Let and be two unit vectors andθ is the angle between them. Then is a unit vector if
(A) (B) (C) (D)
If θ is the angle between two vectors and , then only when
(A) (B)
(C) (D)
Prove that, if and only if are perpendicular, given.
If are mutually perpendicular vectors of equal magnitudes, show that the vector is equally inclined to and.
The scalar product of the vectorwith a unit vector along the sum of vectors and is equal to one. Find the value of.
Let and. Find a vector which is perpendicular to both and, and.
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are.
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors areexternally in the ratio 1: 2. Also, show that P is the mid point of the line segment RQ.
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, find a unit vector parallel to the vector.
Find a vector of magnitude 5 units, and parallel to the resultant of the vectors
.
Find the value of x for whichis a unit vector.
If, then is it true that? Justify your answer.
A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl's displacement from her initial point of departure.
Find the scalar components and magnitude of the vector joining the points
Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.
Area of a rectangle having vertices A, B, C, and D with position vectors and respectively is
(A) (B) 1
(C) 2 (D)
Let the vectors and be such that and, then is a unit vector, if the angle between and is
Find the area of the parallelogram whose adjacent sides are determined by the vector .
Find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and
C (1, 5, 5).
If either or, then. Is the converse true? Justify your answer with an example.
Let the vectors given as . Then show that
Given that and. What can you conclude about the vectors?
Find λ and μ if .
Show that
If a unit vector makes an angleswith with and an acute angle θ with, then find θ and hence, the compounds of.
Find a unit vector perpendicular to each of the vector and, where and.
Find, if and.
Ifis a nonzero vector of magnitude 'a' and λ a nonzero scalar, then λis unit vector if
(A) λ = 1 (B) λ = –1 (C)
(D)
Show that the vectorsform the vertices of a right angled triangle.
Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, -1) are collinear.
If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC. [∠ABC is the angle between the vectorsand]
If either vector, then. But the converse need not be true. Justify your answer with an example.
If are unit vectors such that , find the value of .
If, then what can be concluded about the vector?
Show that is perpendicular to, for any two nonzero vectors
Ifare such thatis perpendicular to, then find the value of λ.
Find, if for a unit vector.
Find the magnitude of two vectors, having the same magnitude and such that the angle between them is 60° and their scalar product is.
Evaluate the product.
Findand, if.
Show that each of the given three vectors is a unit vector:
Also, show that they are mutually perpendicular to each other.
Find the projection of the vectoron the vector.
Find the angle between the vectors
Find the angle between two vectorsandwith magnitudesand 2, respectively having.
If are two collinear vectors, then which of the following are incorrect:
A. , for some scalar λ
B.
C. the respective components of are proportional
D. both the vectors have same direction, but different magnitudes
In triangle ABC which of the following is not true:
A.
C.
D.
Show that the points A, B and C with position vectors,, respectively form the vertices of a right angled triangle.
Find the position vector of the mid point of the vector joining the points P (2, 3, 4) and Q (4, 1, - 2).
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are respectively, in the ration 2:1
Show that the vector is equally inclined to the axes OX, OY, and OZ.
Find the direction cosines of the vector joining the points A (1, 2, -3) and
B (-1, -2, 1) directed from A to B.
Find the direction cosines of the vector
Show that the vectorsare collinear.
Find a vector in the direction of vector which has magnitude 8 units.
Find the unit vector in the direction of vector, where P and Q are the points
(1, 2, 3) and (4, 5, 6), respectively.
Find the unit vector in the direction of the vector.
Find the sum of the vectors
Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (-5, 7).
Find the values of x and y so that the vectors are equal
Write two different vectors having same direction.
Write two different vectors having same magnitude.
Compute the magnitude of the following vectors:
Answer the following as true or false.
(i) andare collinear.
(ii) Two collinear vectors are always equal in magnitude.
(iii) Two vectors having same magnitude are collinear.
(iv) Two collinear vectors having the same magnitude are equal.
In Figure, identify the following vectors.
(i) Coinitial (ii) Equal (iii) Collinear but not equal
Classify the following as scalar and vector quantities.
(i) time period (ii) distance (iii) force
(iv) velocity (v) work done
Classify the following measures as scalars and vectors.
(i) 10 kg (ii) 2 metres north-west (iii) 40°
(iv) 40 watt (v) 10-19 coulomb (vi) 20 m/s2
Represent graphically a displacement of 40 km, 30° east of north.
and
]
sandeep View Answer