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If vecr=l(vecb xx vecc)+m(vecc xx veca)+...

If `vecr=l(vecb xx vecc)+m(vecc xx veca)+n(veca xx vec b)` and `[veca, vecb, vecc]=2,` then `l+m+n` is equal to

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Let veca, vecb, vecc be three vectors such that [(veca, vecb, vecc)]=2 . If vecr=l(vecbxxvecc)+m(veccxxveca)+n(vecaxxvecb) be perpendicular to veca+vecb+vecc , then the value of l+m+n is

For any four vectors veca, vecb, vecc, vecd the expressions (vecb xx vecc).(veca xx vecd) +(vecc xx veca).(vecb xx vecd)+(veca xx vecb).(vecc xx vecd) is always equal to:

If veca, vecb, vecc are non-coplanar vectors, then (veca.(vecb xx vecc))/(vecb.(vecc xx veca)) + (vecb.(vecc xx veca))/(vecc.(veca xx vecb)) +(vecc.(vecb xx veca))/(veca. (vecb xx vecc)) is equal to:

If veca is parallel to vecb xx vecc, then (veca xx vecb) .(veca xx vecc) is equal to

[(veca xxvecb)xx(vecb xx vecc) (vecb xxvecc) xx (vecc xxveca) (veccxxveca) xx (veca xx vecb)] is equal to ( where veca, vecb and vecc are non - zero non- colanar vectors).

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

MCGROW HILL PUBLICATION-VECTOR ALGEBRA-SOLVED EXAMPLES (Numerical Answer Type Questions)
  1. Suppose a and b are two unit vectors and theta is acute angle between ...

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  2. The vector a, b and c are such tha |a|=|b| = 1 and |c|= 2 (ii) a ...

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  3. Let a=2i-3j+4k, b=i+2j-2k " and "c=3i-j+k. Let V be, the volume (in cu...

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  4. If A(3i-2j-k), B(2i+3j-4k), C(-i+j+2k)" and "D(4i+5j+lambdak) are copl...

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  5. Suppose a+x^(2)b+y^(2)c=0" and "a times b+c times a=16(b times c), the...

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  6. Let veca,vecb and vecc be three vectors having magnitudes 1, 1 and 2 r...

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  7. Suppose ABC is a right angled triangle with angleC=pi//2. If abs(AB)=5...

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  8. Let a=5i+4j-k, b=-4i+j+5k, c=i+3j-k. Let alpha be a vector perpendicul...

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  9. If the volume of parallelopiped whose coterminous edges are a=i+j+2k, ...

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  10. Suppose P=(x+1)i+xj+xk, Q=x""i+(x+1)j+xk, k=x""i+xj+(x+1)k are coplana...

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  11. Let abs(a)=sqrt(3), abs(b)=5, b*c=10, angle between b and c is equal t...

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  12. Let a,b,c be three vectors such that a ne 0 and a xx b = 2a xx c,|a|...

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  13. Let a=i-2j+3k. If b is a vector such that a*b=abs(b)^(2)" and "abs(a-b...

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  14. Suppose the diagonals of a parallelogram are represented by vectors i+...

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  15. Let a be vector, such that abs(a)=5. Then abs(a*i)^(2)+abs(a*j)^(2)+ab...

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  16. If vecr=l(vecb xx vecc)+m(vecc xx veca)+n(veca xx vec b) and [veca, v...

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  17. Suppose a=5i-3j+2k, b=-i+2j+3k, c=7i-18j+21k," then "[a-b" "b-c" "c-a]...

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  18. If a=2i-3j+5k, b=3i-4j+5k" and "c=5i-3j-2k then volume of the parallel...

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  19. Suppose a, b, c are three unit vectors such that " "abs(a-b)^(2)...

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  20. If 4x+3y+12z=26, x, y, z, in R, then minimum possible value of x^(2)+y...

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