The resultant of two forces P N and 3 N is a force of 7 N. If the direction of 3 N force were reversed, the resultant would be 19N. The value of P is
Prove that vectors u=(al+a1l1)i^+(am+a1m1)j^+(an+a1n1)k^ v=(bl+b1l1)i^+(bm+b1m1)j^+(bn+b1n1)k^ w=(bl+b1l1)i^+(bm+b1m1)j^+(bn+b1n1)k^ are coplanar.
If a,bandc are non-cop0lanar vector, then that prove ∣∣(ad˙)(b×c)+(bd˙)(c×a)+(cd˙)(a×b)∣∣ is independent of d,wheree is a unit vector.
Given three points are A(−3,−2,0),B(3,−3,1)andC(5,0,2)˙ Then find a vector having the same direction as that of AB and magnitude equal to ∣∣AC∣∣˙
If aandb are two unit vectors and θ is the angle between them, then the unit vector along the angular bisector of a and b will be given by a. cos(θ/2)a−b b. 2cos(θ/2)a+b c. 2cos(θ/2)a−b d. none of these
The position vectors of the vertices A,BandC of a triangle are three unit vectors a,b,andc, respectively. A vector d is such that da˙=db˙=dc˙andd=λ(b+c)˙ Then triangle ABC is a. acute angled b. obtuse angled c. right angled d. none of these
A pyramid with vertex at point P has a regular hexagonal base ABCDEF , Positive vector of points A and B are i^andi^+2j^ The centre of base has the position vector i^+j^+3k^˙ Altitude drawn from P on the base meets the diagonal AD at point G˙ find the all possible position vectors of G˙ It is given that the volume of the pyramid is 63 cubic units and AP is 5 units.
If vectors AB=−3i^+4k^andAC=5i^−2j^+4k^ are the sides of aDeltaABC, then the length of the median through Ais a. 14 b. 18 c. 29 d. 5