Classify the following measures as scalars and vectors.(i) 10 kg (ii) 2 meters north-west (iii) 40∘(iv) 40 watt (v) 10−19 coulomb (vi)20 m/s2
If a ,b ,c ,d are the position vector of point A,B,C and D , respectively referred to the same origin O such that no three of these point are collinear and a + c = b + d , than prove that quadrilateral ABCD is a parallelogram.
In a trapezium, vector BC=αAD˙ We will then find that p=AC+BD is collinear withAD˙ If p=μAD, then which of the following is true? a. μ=α+2 b. μ+α=2 c. α=μ+1 d. μ=α+1
The position vectors of the vertices A,B,andC of a triangle are i^+j^,j^+k^andi^+k^ , respectively. Find the unite vector r^ lying in the plane of ABC and perpendicular to IA,whereI is the incentre of the triangle.
The vectors xi^+(x+1)j^+(x+2)k^,(x+3)i^+(x+4)j^+(x+5)k^and(x+6)i^+(x+7)j^+(x+8)k^ are coplanar if x is equal to a. 1 b. −3 c. 4 d. 0
In triangle ABC,∠A=300,H
is the orthocenter and D
is the midpoint of BC.
is produced to T
such that HD=DT
The length AT
is equal to
(d). none of these
If a,b,c are non-coplanar vector and λ is a real number, then the vectors a+2b+3c,λb+μcand(2λ−1)c are coplanar when a. μ∈R b. λ=21 c. λ=0 d. no value of λ