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If vector vec(A)=hat(i)+2hat(j)+4hat(k) ...

If vector `vec(A)=hat(i)+2hat(j)+4hat(k)` and `vec(B)=5hat(i)` represent the two sides of a triangle, then the third side of the triangle can have length equal to

A

`ssqrt(56)`

B

`sqrt(21)`

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
A
`vec(A)+vec(B)+vec(C)=0`
So, `" " hat(i)+2hat(j)+4hat(k)+5hat(i)+vec(C)=0`
`vec(C)=-6hat(i)-2hat(j)-4hat(k)`
`|vec(C)|=sqrt(36+4+16)=sqrt(56)`
Hence A
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BANSAL-UNIT DIMENSION, VECTOR & BASIC MATHS-EXERCISE - 1 [SINGLE CORRECT CHOICE TYPE]
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  2. which of the following is not true ? If vec(A)=3hat(i)+4hat(j) and vec...

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  3. If vector vec(A)=hat(i)+2hat(j)+4hat(k) and vec(B)=5hat(i) represent t...

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  4. If vec(a) be a unit vector, then :-

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  5. If two numerical equal forces P and P acting at a point produce a resu...

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  6. Given that vec(A)+vec(B)=vec(R) and vec(A)+2vec(B) is perpendicular...

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  10. The angle subtended by vector vec(i)+vec(j) with x-axis is :-

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  11. Moment about point whose coordinate is (1,2,3) of a force represented ...

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  12. If vec(A) and vec(B) denote the sides of a parallelogram and its area ...

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  13. A vector perpendicular to (hat(i)+hat(j)+hat(k)) and (hat(i)-hat(j)-...

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  14. The unit vector along vec(i)+vec(j) is :-

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  15. Two constant forces vec(F)(1) and vec(F)(2) acts on a body of mass 8 k...

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  16. Figure shows three vectors a, b and c. If RQ=2PR, which of the followi...

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  17. Component of -10hat(j) in the direction of 3hat(i)-4hat(j) is :-

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  18. If 3hat(i)-2hat(j)+8hat(k) and 2hat(i)+xhat(j)+hat(k) are at right ...

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  19. If vec(a)=4hat(i)+hat(j)-hat(k) , vec(b)=3hat(i)-2hat(j)+2hat(k) , the...

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  20. Write a force of 10 N in x-y plane in terms of unit vectors hat(i) a...

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