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

Find the value of x for which `x(hati+hatj+hatk)` is a unit vector.

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The correct Answer is:
`+-(1)/(sqrt(3))`
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Find the value of a so that the four points with position vectors -hatj+hatk,2hati-hatj-hatk,hati+lambdahatj+hatk and 3hatj+3hatk are co-plannar.

Find the angle of vector veca=6hati+2hatj-3hatk with x -axis.

Find the projection of the vector 7hati+hatj-4hatk on the vector 2hati+6hatj+3hatk .

Find the projection of the vector hati+3hatj+7hatk on the vector 7hati-hatj+8hatk .

The scalar product of the vector hati+hatj+hatk with a unit vector along the sum of vectors 2hati+4hatj-5hatk and lambda hati+2hatj+3hatk is equal to one. Find the value of lambda .

Find the value of c for which the vectors vec(a)=(c log_(2)x)hati-6hatj+3hatk and vec(b)=(log_(2)x)hati+2hatj+(2c log_(2)x)hatk makes an obtuse angle for any (x in 0, oo) .

If vecA=2hati-2hatj-hatk and vecB=hati+hatj , then : (a) Find angle between vecA and vecB . (b) Find the projection of resultant vector of vecA and vecB on x-axis. (c) Find a vector which is, if added to vecA , gives a unit vector along y-axis.

If vecA= 6hati- 6hatj+5hatk and vecB= hati+ 2hatj-hatk , then find a unit vector parallel to the resultant of vecA & vecB .

The values of x for which the angle between the vectors veca =xhati - 3hatj-hatk and vecb = 2x hati + x hatj -hatk is acute, and the angle, between the vector vecb and the axis of ordinates is obtuse, are

NCERT GUJARATI-VECTOR ALGEBRA-Miscellaneous Exercise on chapter 10
  1. Write down a unit vector in XY-plane, making an angle of 30^(@) with t...

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  2. Find the scalar components and magnitude of the vector joining the poi...

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  3. A girl walks 4 km towards west, then she walks 3 km in a direction 30^...

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  4. If veca=vecb+vecc , then is it true that |veca|=|vecb|+|vecc|? Justify...

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  5. Find the value of x for which x(hati+hatj+hatk) is a unit vector.

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  6. A vector has magnitude 5 units. It is parallel to the resultant vector...

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  7. If veca=hati+hatj+hatk,vecb=2hatj-hatj+3hatkandvecc=hati-2hatj+hatk, ...

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  8. Show that the points A(1,-2,-8),B(5,0,-2)andC(11,3,7) are collinear , ...

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  9. Find the position vector of a point R which divides the line joining t...

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  10. The two adjacent sides of a parallelogram are 2hati-4hatj+5kandhati-2h...

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

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  12. Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatkandvecc=2hati-hatj+4ha...

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  13. The scalar product of the vector hati+hatj+hatk with a unit vector alo...

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

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  15. If theta is angle between two vectors vec(a) and vec(b) then vec(a).ve...

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  16. Let vec(a) and vec(b) be two unit vectors and theta is the angle betwe...

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  17. The value of hati.(hatjxxhatk)+hatj*(hatixxhatk)+hatk*(hatixxhatj) is

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  18. If theta is the angle between any two vectors vecaandvecb, then |veca*...

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