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
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ABC is a triangle and P any point on BC. if PQ
is the sum of AP
, show that ABPQ is a parallelogram and Q , therefore , is a fixed point.
If the projections of vector a
- and z
-axes are 2, 1 and 2 units ,respectively, find the angle at which vector a
is inclined to the z
,than prove that B is the midpoint of AC.
are two non-collinear vectors, prove that the points with position vectors a+b,a−b
are collinear for all real values of λ˙
If in parallelogram ABCD, diagonal vectors are AC=2i^+3j^+4k^
then find the adjacent side vectors AB
The position vectors of the point A,B,CandDare3i^−2j^−k^,2i^+3j^−4k^,−i^+j^+2k^
respectively. If the points A,B,CandD
lie on a plane, find the value of λ˙
In a quadrilateral PQRS,PQ=a,QR,b,SP=a−b,M
is the midpoint of QRandX
is a point on SM
such that SX=54SM˙
Prove that P,XandR
Find the point of intersection of AB and A(
6,-7,0),B(16,-19,-4,) , C(0,3,-6) and D(2,-5,10).