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Find the value of x for which x( hat i+...

Find the value of x for which `x( hat i+ hat j+ hat k)`is a unit vector.

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To find the value of \( x \) for which \( x(\hat{i} + \hat{j} + \hat{k}) \) is a unit vector, we can follow these steps: ### Step 1: Define the Vector Let the vector be defined as: \[ \mathbf{A} = x(\hat{i} + \hat{j} + \hat{k}) = x\hat{i} + x\hat{j} + x\hat{k} \] ...
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For what value of p , is ( hat i+ hat j+ hat k)p a unit vector?

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Find the value of ' p ' for which the vectors 3 hat i+2 hat j+9 hat k\ a n d\ hat i-2p hat j+3 hat k are parallel.

The scalar product of the vector vec a= hat i+ hat j+ hat k with a unit vector along the sum of the vectors vec b=2 hat i+4 hat j-5 hat k\ a n d\ vec c=lambda hat i+2 hat j+3 hat k is equal to 1. Find the value of lambda and hence find the unit vector along vec b+ vec cdot

Find the values of x and y if the vectors vec a=3 hat i+x hat j- hat k and vec b=2 hat i+ hat j+y hat k are mutually perpendicular vectors of equal magnitude.

Find the values of a for which are vectors vecalpha= hat i+2 hat j+ hat k , vecbeta=a hat i+ hat j+2 hat k\ a n d\ vecgamma= hat i+2 hat j+a hat k are coplanar. \

Find the value of lambda for which the four points with position vectors - hat j- hat k ,4 hat i+5 hat j+lambda hat k ,3 hat i+9 hat j+4 hat k and 4 hat i+4 hat j+4 hat k are coplanar.

The magnitude of the vector product of the vector hat i+ hat j+ hat k with a unit vector along the sum of vectors 2 hat i+4 hat j-\ 5 hat k and lambda hat i+2 hat j+3 hat k is equal to sqrt(2) . Find the value of lambda .

Find the resultant of vectors vec a= hat i- hat j+2 hat k and vec b= hat i+2 hat j-4 hat kdot Find the unit vector in the direction of the resultant vector.

Find the projection of the vector hat i+3 hat j+7 hat k on the vector 7 hat i- hat j+8 hat k

NCERT ENGLISH-VECTOR ALGEBRA-MISCELLANEOUS EXERCISE
  1. If theta is the angle between any two vectors veca and vec b, then...

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  2. The two adjacent sides of a parallelogram are 2 hat i-4 hat j+5 hat k ...

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  3. Show that the direction cosines of a vector equally inclined to the a...

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  4. Write down a unit vector in XY-plane, making an angle of 30° with the...

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  5. A girl walks 4 km towards west, and then she walks 3 km in a direction...

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  6. Find the scalar components and magnitude of the vector joining the po...

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  7. Find the value of x for which x( hat i+ hat j+ hat k)is a unit vector...

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  8. Let vec a= hat i+4 hat j+2 hat k , vec b=3 hat i-2 hat j+7 hat k and...

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  9. The scalar product of the vector hat i+ hat j+ hat kwith a unit vect...

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  10. If theta is the angle between two vectors veca and vecb, then veca...

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  11. Let veca and vecb be two unit vectors and is the angle between th...

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  12. If -> a , -> b , -> care mutually perpendicular vectors of equal ma...

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  13. Prove that (veca+ vecb)*( veca+ vecb)=|veca|^2+| vecb|^2, if and only ...

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  14. The value of hat i *( hat jxx hat k)+ hat j*( hat ixx hat k)+ hat k*...

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  15. यदि veca= vecb + vecc, तब क्या यह सत्य है कि | |veca| = |vecb| +|vecc|...

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  16. Find the position vector of a point R which divides the line joinin...

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  17. If veca= hat i+ hat j+ hat k, vecb=2 hat i- hat j+3 hat k and vecc...

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  18. Find a vector of magnitude 5 units, and parallel to the resultant of ...

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  19. Show that the points A(1,-2,-8) , B(5,0,-2) and C(11,3,7) are colline...

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