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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 (B. Fill in the Blanks)
  1. The magnitude of projection of (2hat(i)-hat(j)+hat(k)) " on" (hat(i)-2...

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  2. Vector of magnitude 5 units and in the direction opposite to 2hat(i)+3...

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  3. Find the sum of vectors vec a= hat i-2 hat j+ hat k ,\ vec b=-2 hat ...

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  4. The value of 'a' when the vectors : 2hat(i)-3hat(j)+4hat(k) and a...

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  5. If vec(a)=2hat(i)+hat(j)-2hat(k), then |vec(a)|= .

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  6. The direction - ratios of the vector vec(a)=6hat(i)-3hat(j)+2hat(k) ar...

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  7. Find the projection of the vector hat i- hat jon the vector hat i+ ...

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

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  9. If vec(p) is a unit vector and (vec(x)-vec(p)).(vec(x)+vec(p))=80, the...

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  10. Angle between hat(i)-hat(j) and hat(j)-hat(k) is .

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  11. Find the value of : (i) (hat(i) xxhat(j))*hat (k) + hat(i)* hat(j) ...

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  12. (hat(k)xx hat(j)).hat(i)+hat(j).hat(k)= ………….

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  13. (hat(k)xx hat(i)).hat(j)+hat(i).hat(k) …………..

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

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  15. The magnitude of vec(a)xx vec(b) if vec(a)=2hat(i)+hat(k) and vec(b)...

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  16. If any two of three vectors vec(a), vec(b), vec(c ) are parallel, then...

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  17. The value of 'lambda' such that the vectors : 3hat(i)+lambdahat(j)+5...

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