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The number of vectors of unit length ...

The number of vectors of unit length perpendicular to vectors ` vec a=(1,1,0)a n d vec b=(0,1,1)` is a. one b. two c. three`` d. infinite

A

one

B

two

C

three

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
b
we know that if `hatn` is perpendicular to `veca` as we as `vecb` .then
`hatn=(vecaxxvecb)/(|vecaxxvecb|)or (vecbxxveca)/(|vecbxxveca|)`
As ` veca xx vecb and vecb xx veca` represent two vectors in opposite directions , we have two possible value of `hatn`.
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. Let bar(PR)=3hati+hatj-2hatk and bar(SQ)=hati-3hatj-4hatk determine d...

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  3. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(2)hatj+b(3)hatk and vecc=c(...

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  4. The number of vectors of unit length perpendicular to vectors vec ...

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  5. veca=2hati-hatj+hatk,vecb=hatj+2hatj-hatk,vecc=hati+hatj -2 hatk . A v...

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  6. For three vectors vec u , vec va n d vec w which of the following exp...

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  7. Which of the following expressions are meaningful? a. vec u ( vec vx...

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  8. Let A={2,3,4}, B={7,8,9,10} and f={(2,7),(3,8),(4,9)} be a function f...

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  9. Vector 1/3 (2hati - 2hatj +hatk) is

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  10. Let vec A be a vector parallel to the line of intersection of plan...

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  11. The unit vector parallel to the resultant of the vectors hati+hatj+hat...

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  12. Let vecx,vecy and vecz be three vector each of magnitude sqrt(2) an...

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  13. Let Delta PQR be a triangle Let veca=bar(QR),vecb=bar(RP)and vecc=b...

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  14. Draw the graph of y=loge(−x), flip the graph of y=loge x over the y-ax...

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  15. Find the derivative of y = ln x^2

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  16. Find the derivative of y = 2 ln (3x^2 − 1)

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  17. If veca and vecb are vectors in space given by veca=(hati-2hatj)/(sqrt...

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  18. Let veca=-hati-hatk,vecb =-hati + hatj and vecc =hat i + 2hatj + 3hatk...

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  19. If veca, vecb and vecc are unit vectors satisfying |veca-vecb|^(2)+|ve...

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  20. Let veca,vecb,and vecc be three non-coplanar ubit vectors such the ...

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