If vectors a=i^+2j^−k^,b=2i^−j^+k^andc=lambdai^+j^+2k^ are coplanar, then find the value of (λ−4)˙
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∣∣˙
Lett α,βandγ be distinct real numbers. The points whose position vector's are αi^+βj^+γk^;βi^+γj^+αk^andγi^+αj^+βk^
A vector has components p and 1 with respect to a rectangular Cartesian system. The axes are rotted through an angel αabout the origin the anticlockwise sense. Statement 1: IF the vector has component p+2and 1 with respect to the new system, then p=−1. Statement 2: Magnitude of the original vector and new vector remains the same.
′I′ is the incentre of triangle ABC whose corresponding sides are a,b,c, rspectively. aIA+bIB+cIC is always equal to a. 0 b. (a+b+c)BC c. (a+b+c)AC d. (a+b+c)AB
If the resultant of three forces F1=pi^+3j^−k^,F2=6i^−k^andF3=−5i^+j^+2k^ acting on a parricle has magnitude equal to 5 units, then the value of p is a. −6 b. −4 c. 2 d. 4