let a=i^+j^+2k^ b=b1i^+b2J^+2k^ c=5i^+j^+2k^ & (a+b) is perpendicular to c and projection vector of b on a is a then find ∣∣b∣∣ (a) 6 (b) 22 (c) 32 (d) 11
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Find a vector of magnitude 5 units, and parallel to the resultant of the vectors a=2i^+3j^−k^ and b=i^−2j^+k^.
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are i^+2j^−k^and −i^+j^+k^respectively, in the ratio 2 : 1(i) internally (ii) externally
If a= i^+j^+k^,b=2i^−j^+3k^ and c=i^−2j^+k^find a unit vector parallel to the vector 2a−b+3c.
Find the area of a triangle having the pointsA(1,1,1), B(1,2,3)and C(2,3,1)as its vertices.
Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).
If ais a nonzero vector of magnitude a and λa nonzero scalar, then λais unit vector if(A) λ=1 (B) λ=−1 (C) a=∣λ∣ (D) a=∣λ∣1
Prove that (a+b)⋅(a+b)=∣a∣2+∣∣b∣∣2, if and only if a,bare perpendicular, given a=0,b=0
Write two different vectors having same direction.