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The volume of the parallelopiped whose...

The volume of the parallelopiped whose sides are given by `overset(to)(OA)= 2hat(i) -3hat(j) , overset(to)(OB) +hat(i) + hat(j) -hat(k)`
`overset(to)(OC)= 3hat(i) -hat(k) ,` is

A

`4//13`

B

4

C

`2//7`

D

none of these

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The correct Answer is:
B
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Find the volume of the parallelopiped whose coterminus edges are given by vectors 2hat(i)+3hat(j)-4hat(k),5hat(i)+7hat(j)+5hat(k)and4hat(i)+5hat(j)-2hat(k) .

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors vec(a)=2hat(i)-3hat(j)+hat(k),vec(b)=hat(i)-hat(j)+2hat(k) and vec(c)=2hat(i)+hat(j)-hat(k) .

Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) vec(a)=hat(i) + 2 hat(j)+ 3 hat(k) and vec(b)=-3 hat(i)- 2 hat(j) + hat(k) (ii) vec(a)=(3 hat(i)+hat(j) + 4 hat(k)) and vec(b)= ( hat(i)- hat(j) + hat(k)) (iii) vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j) (iv) vec(b)= 2 hat(i) and vec(b) = 3 hat(j).

The area of the parallelogram whose sides are represented by the vector hat(j)+3hat(k) and hat(i)+2hat(j)-hat(k) is

Find the area of parallelogram whose adjacent sides are represented by the vectors 3hat(i)+hat(j)-2hat(k) and hat(i)-2hat(j)-hat(k) .

Find the volume of the parallelopiped whose coterminus edges are : (1) 3hat(i)+5hat(k),4hat(i)+2hat(j)-3hat(k),3hat(i)+hat(j)+4hat(k) (2) bar(a)=hat(i)+hat(j),bar(b)=hat(j)+hat(k),bar(c)=hat(k)+hat(i) (3) 2hat(i)+5hat(j)-4hat(k),5hat(i)+7hat(j)+5hat(k),4hat(i)+5hat(j)-2hat(k) .

MCGROW HILL PUBLICATION-VECTOR ALGEBRA-EXERCISE (Level-1 Single Correct Answer Type Questions)
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  9. Area of the parallelogram on the vectors a + 3b and 3a + b if abs(a)=a...

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  10. If a=x""i+5j+7k, b=i+j-k, c=i+2j+2k are coplanar then the value of x i...

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  11. If a*(b times c)=3 then

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  12. Let a=2i+2j+k and b be another vector such that a*b=14" and "a times b...

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  13. ABCDEF is a regular hexagon with centre a the origin such that vec(AB)...

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  15. Let P ,Q ,R and S be the points on the plane with position vectors ...

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  16. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb)*(...

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  17. The edges of a parallelopiped are of unit length and are parallel to ...

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