Related InterviewSolutions

• If ABCDE is a pentagon, then `vec(AB) + vec(AE) + vec(BC) + vec(DC) + vec(ED) + vec(AC) ` is equal toA. `4 vec(AC)`B. `2 vec(AC)`C. `3vec(AC)`D. `5 vec(AC)`
• Prove that 1,1,1 cannot be direction cosines of a straight line.
• If ABCD is a quadrilateral, then `vec(BA) + vec(BC)+vec(CD) + vec(DA)=`A. `2 vec(BA)`B. `2 vec(AB)`C. `2vec(AC)`D. `2(BC)`
• If `P`is a pointand `A B C D`is aquadrilateral and ` vec A P+ vec P B+ vec P D= vec P C`, show that `A B C D`is aparallelogram.
• A vector ` vec r`is inclinedat equal acute angles of `x-a xi s ,``y-a xi s`and `z-a xi sdot`if `| vec r|=6`units, find ` vec rdot`
• Prove that the sum of threevectors determined by the medians of a triangle directed from the vertices iszero.
• A, B have vectors ` vec a , vec b ` relative to the origin O and X, Y divide ` vec(AB)` internally and externally respectively in the ratio `2:1` . Then , `vec (XY)=`A. `(3)/(2) (vec b - vec a) `B. `(4)/(3) (vec a - vec b) `C. `(5)/(6) (vec b - vec a) `D. `(4)/(3) (vec b - vec a) `
• G is a point inside the plane of the triangle `ABC, vecGA + vecGB + vecGC=0`, then show that G is the centroid of triangle ABC.A. `vec(0)`B. `3vec(GA)`C. `3 G vec(B)`D. `3 vec(GC)`
• If A, B, C are vertices of a triangle whose position vectors are `vec a, vec b and vec c` respectively and G is the centroid of `Delta ABC, " then " vec(GA) + vec(GB) + vec(GC),` isA. `vec 0`B. `veca + vec b + vec c `C. `(veca + vec b + vec c )/(3)`D. `(veca - vec b - vec c )/(3)`
• If the position vectors of the vertices of a triangle of a triangle are `2 hati - hatj + hatk , hati - 3 hatj - 5 hatk and 3 hati -4 hatj - 4 hatk ,` then the triangle isA. equilateralB. isoscelesC. right angled but not isoscelesD. right angled