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अदिश राशि (Scaler Quantities)|सदिश राशि (Vector Quantities)|सदिशों की आवश्यकता (Need of Vectors)|सदिश का निरूपण|सदिशों का संकेतन|सदिशों का मापांक (Modulus of Vectors)|सदिशों के प्रकार (Types of Vectors)|सदिशों का योग (Addition of Vectors)|सदिशों के योग का त्रिभुज तथा चतुर्भुज नियम (Triangle and Parellelogram Law of Vector Addition)

सदिशों का अदिश गुणनफल (Scalar Product of Vectors)|तीन विमाओं में दो सदिशों का अदिश गुणनफल (Product of Two Vectors in Three Dimensions)|भौतिकी में अदिश गुणनफल के उदाहरण (Examples of Scalar Product in Physics)|प्रश्न (Question)|सदिशों का सदिश गुणनफल (Vector Product of Vectors)|तीन विमाओं में दो सदिशों का सदिश गुणनफल (Cross Product of Two Vectors in Three Dimensions)|प्रश्न (Question)

Let P_1 denote the equation of a plane to which the vector ( hat i+ hat j) is normal and which contais the line whose equation is vec r= hat i+ hat j+ hat k+lambda( hat i- hat j- hat k)a n dP_2 denote the equation of the plane containing the line L and a point with position vector hat jdot Which of the following holds good? a. The equation of P_1 is x+y=2. b. The equation of P_2 is vec(r) . (i-2j+k) = 2 c. The acute angle between P_1 and P_2 is cot^(-1) sqrt(3) d. The angle between plane P_2 and the line L is tan^(-1) sqrt(3)

The ratio of boys to girls in a class is 2 : 3 and the average score of all the students in the class in maths is 54. The average score of boys is 50% more than that of girls. What is the average score of girls ? एक कक्षा में लड़के और लड़कियों की संख्या का अनुपात 2 : 3 है और कक्षा में सभी छात्रों के गणित में औसत प्राप्तांक 54 है | लड़कों का औसत प्राप्तांक लड़कियों के औसत प्राप्तंक से 50% अधिक है | लड़कियों का औसत प्राप्तांक कितना है ?

If matrix A=[[1,2,3], [4,1,2], [1,-1,2]] B= [[2,1,3], [4,1,-1], [2,2,3]] C= [[14], [12], [2]] D= [[13], [11], [14]]. When X= [[x], [y],[z]] is such that solutions of equations AX=C and BX=D represents two points L and M in three dimensional space. If l' and M' are the reflection of points L and M in the plane x+y+z=9 then find values of L,M,L' and M'

The intersection of the planes 2x-y-3z=8 and x+2y-4z=14 is the line L .The value of alpha for which the line L is perpendicular to the line through (alpha, 2,2) and (6,11,-1) is :

The ratio of the number of boys in sections A and B of a class is 2 : 3 and the ratio between the total number of boys and girls in sections A and B is 3 : 4. If the number of girls in B is 50% of the number of boys in B, then what will be the ratio between the number of girls in A and B ? एक कक्षा के अनुभाग A और B में लड़कों की संख्या का अनुपात 2:3 है तथा अनुभाग A और B में लड़कों और लड़कियों की कुल संख्या का अनुपात 3:4 है | यदि 8 में लड़कियों की संख्या, B में लड़कों की संख्या की 50% है, तो A और B में लड़कियों की संख्या का अनुपात कितना होगा ?

Any first degree equation in x, y and z represents a plane i.e., ax+by+cz+d=0 is the general equation of a plane. If p be the length of perpendicular from the origin to a plane and d.c. of this normal is lt l, m n gt , then the equation of the plane in the normal form is lx+my+nz=p_(1) . Vector equation of a plane passing through a point having position vector vec(a) and normal to vector vec(n) is (vec(r)-vec(a))vec(n)=0" or "vec(r).vec(n)=vec(a).vec(n) Suppose a vector vec(n) of magnitude 2sqrt(3) such that it makes equal acual angles with the co-ordinate axes. If vec(n) is a normal to the plane containing the point (1,-1,2) . The vector vec(n) is equal to