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Let vec a=2 hat i- hat j+ hat k , vec b...

Let ` vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d vec c= hat i+ hat j-2 hat k` be three vectors. A vector in the plane of ` vec ba n d vec c` , whose projection on ` vec a` is of magnitude `sqrt(2//3)` , is `2 hat i+3 hat j-3 hat k` b. `2 hat i-3 hat j+3 hat k` c. `-2 hat i- hat j+5 hat k` d. `2 hat i+ hat j+5 hat k`

A

`2hat(i)+3hat(j)-3hat(k)`

B

`2hat(i)+3hat(j)+3hat(k)`

C

`-2hat(i)-hat(j)+5hat(k)`

D

`2hat(i)+hat(j)+5hat(k)`

Text Solution

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The correct Answer is:
A, C
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Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d vec c= hat i+ hat j-2 hat k be three vectors. A vector in the plane of vec ba n d vec c , whose projection on vec a is of magnitude sqrt(2//3) , is a. 2 hat i+3 hat j-3 hat k b. 2 hat i-3 hat j+3 hat k c. -2 hat i- hat j+5 hat k d. 2 hat i+ hat j+5 hat k

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ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (More Than One Correct Option Type Questions)
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  2. Given three vectors U=2hat(i)+3hat(j)-6hat(k), V=6hat(i)+2hat(j)+2hat(...

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  3. Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d ve...

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  4. Three vectors veca,vecb,vecc are such that vecaxxvecb= 3(vecaxxvecc)Al...

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  5. Let a, b and c be non-zero vectors and |a|=1 and r is a non-zero vecto...

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  6. If veca and vecb are two unit vectors perpendicular to each other and...

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  7. Given three non-coplanar vectors OA=a, OB=b, OC=c. Let S be the centre...

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  8. If a=hat(i)+hat(j)+hat(k) and b=hat(i)-hat(j), then the vectors (a*hat...

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  9. If vec a=x hat i+y hat j+z hat k , vec b=y hat i+z hat j+x hat k and v...

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  10. If veca, vecb, vecc are three non-zero vectors, then which of the foll...

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  11. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

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  12. If a, b, c are three non-zero vectors, then which of the following sta...

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  13. Let veca and vecb be two non- zero perpendicular vectors. A vector vec...

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  14. If veca and vecb are any two unit vectors, then find the greatest post...

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  15. If a is perpendicular to b and p is non-zero scalar such that pr+(r*b)...

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  16. In a four-dimensional space where unit vectors along the axes are h...

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  17. A vector(d) is equally inclined to three vectors a=hat(i)-hat(j)+hat(k...

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  18. If a, b, c are non-zero, non-collinear vectors such that a vectors suc...

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  19. Given three vectors veca, vecb and vecc are non-zero and non-coplanar ...

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  20. If r=hat(i)+hat(j)+lambda(2hat(i)+hat(j)+4hat(k)) and r*(hat(i)+2hat(j...

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