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Find lambda if (2 hat i+6 hat j+14 hat k...

Find `lambda` if `(2 hat i+6 hat j+14 hat k)x\ ( hat i-\ lambda hat j+7 hat k)= vec0`

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Find lambda if (2hat i+6hat j+14hat k)xx(hat i-lambdahat j+7hat k)=vec 0

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The shortest distance between the line L_1=(hat i - hat j hat k) lambda (2 hat i - 14 hat j 5 hat k) and L_2=(hat j hat k) mu (-2 hat i - 4 hat 7 hat) then L_1 and L_2 is

Find 'lambda' and 'mu' if : (hat(i)+3hat(j)+9hat(k))xx(3hat(i)-lambda hat(j)+mu hat(k))=hat(0) .

The line through hat i+3 hat j+2 hat k and _|_ to the line vec r=( hat i+2 hat j- hat k)+lambda(2 hat i+ hat j+ hat k)a n d vec r=(2 hat i+6 hat j+ hat k)+mu( hat i+2 hat j+3 hat k) is a. vec r=( hat i+2 hat j- hat k)+lambda(- hat i+5 hat j-3 hat k) b. vec r= hat i+3 hat j+2 hat k+lambda( hat i-5 hat j+3 hat k) c. vec r= hat i+3 hat j+2 hat k+lambda( hat i+5 hat j+3 hat k) d. vec r= hat i+3 hat j+2 hat k+lambda(- hat i-5 hat j-3 hat k)

Find the equation of the line passing through the point hat i+ hat j- hat k and perpendicular to the lines vec r= hat i+lambda(2 hat i+ hat j-3 hat k)a n d vec r=(2 hat i+ hat j- hat k)dot

If vec(a) = 2 hat(i) + 6 hat(j) + 3hat(k) , vec(b) = hat(i) + lambda hat(j) + mu hat(k) . If vec (a) xx vec(b) = 0 , find the value of lambda and mu .

Find the angle between the following pairs of lines: (i) quad vec r=2hat i-5hat j+hat k+lambda(3hat i+2hat j+6hat k) and vec r=3hat i+hat j-2hat k+lambda(hat i-hat j-2hat k)vec r=3hat i+hat j-26hat k+mu(3hat i-5hat j-2hat k)

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MODERN PUBLICATION-VECTOR ALGEBRA -Objective Type Questions (D. Very Short Answers Type Questions)
  1. For what value of 'a' the vectors : 2hat(i)-3hat(j)+4hat(k) and a h...

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  2. Write a unit vector in the direction of vec P Q ,\ w h e r e\ P\ a n ...

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  3. In a triangle OAC, if B is the mid point of side AC and vec O A= vec ...

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  4. Find the position vector of the point, which divides the join of point...

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  5. If |vec(a).vec(b)|=|vec(a)xx vec(b)|, find the angle between vec(a) an...

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  6. Obtain the dot product of the vectors : vec(a)=hat(i)-hat(j)+hat(k) ...

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  7. Write the magnitude of the vector vec(a) in terms of dot product.

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  8. Let vec(a)=(2hat(i)+3hat(j)+2 hat(k)) and vec(b)=(hat(i)+2hat(j)+hat(k...

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  9. Evaluate : (3vec(a)-5vec(b)).(2vec(a)+7vec(b)).

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  10. If vec a is a unit vector and (vec x - vec a).(vec x + vec a)=8, then ...

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  11. Find the angle between hat(i)+hat(j)+hat(k) and hat(i)+hat(j)-hat(k).

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  12. Find the angle between vec(a) and vec(b) such that : |vec(a)|=sqrt(2...

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  13. The position vectors of three vectors A, B and C are given to be hat(i...

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  14. Find 'lambda' when the vectors : vec(a)=2hat(i)+lambda hat(j)+hat(k) ...

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  15. If vec(a) and vec(b) are perpendicular vectors, |vec(a)+vec(b)|=3 and ...

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  16. Find the magnitude of each of the two vectors veca and vec b having th...

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  17. Find lambda if (2 hat i+6 hat j+14 hat k)x\ ( hat i-\ lambda hat j+7 h...

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  18. Find a vector of magnitude sqrt(171) which is perpendicular to both of...

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  19. If vec(a)=2hat(i)+3hat(j)+hat(k), vec(b)=hat(i)-2hat(j)+hat(k) and v...

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  20. Find the value of 'lambda' such that the vectors : 3hat(i)+lambda hat(...

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