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The position vector of a point P is r=xh...

The position vector of a point P is `r=xhat(i)+yhat(j)+hat(k)z,` where `x, y, zinN and a=hat(i)+2hat(j)+hat(k). If r*a=20` and the number of possible of P is `9lambda`, then the value of `lambda` is

A

`81`

B

`49`

C

`100`

D

`36`

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A
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ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Single Option Correct Type Questions)
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  2. If a, b and c are any three non-zero vectors, then the component of at...

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  3. The position vector of a point P is r=xhat(i)+yhat(j)+hat(k)z, where x...

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  4. . Let a, b > 0 and vecalpha=hati/a+4hatj/b+bhatk and beta=bhati+ahatj+...

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  5. If veca, vecb and vecc are any three vectors forming a linearly indepe...

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  6. Two adjacent sides of a parallelogram ABCD are given by vec(AB)=2hati+...

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  7. If in a triangleABC, BC=(e)/(|e|)-(f)/(|f|) and AC=(2e)/(|e|): |e|ne|f...

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  8. Let the unit vectors a and b be perpendicular and the unit vector c be...

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  11. A line makes an angle theta both with x-axis and y-axis. A possible ra...

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  12. Let veca, vecb and vecc be the three vectors having magnitudes, 1,5 an...

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  13. Find the perpendicular distance of a corner of a unit cube from a dia...

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  14. If p,q are two-collinear vectors such that (b-c)ptimesq+(c-a)p+(a-b)q...

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  15. Let a=hat(i)+hat(j)+hat(k), b=-hat(i)+hat(j)+hat(k), c=hat(i)-hat(j)+h...

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  16. A parallelepiped is formed by planes drawn parallel to coordinate axes...

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  17. Let bar a,bar b,bar c be three non-coplanar vectors and bar d be a no...

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  18. If alpha(atimesb)+beta(btimesc)+gamma(ctimesa)=0, then

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  19. Let area of faces triangleOAB=lambda1, triangleOAC=lambda2, triangleOB...

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  20. Given four non zero vectors bar a,bar b,bar c and bar d. The vectors ...

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