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What is the area of the rectangle having...

What is the area of the rectangle having vertices A, B, C and D with positive vectors `-hat(i)+(1)/(2) hat(j)+4hat(k), hat(i)+(1)/(2)hat(j)+4hat(k), hat(i)-(1)/(2) hat(j)+4hat(k) and -hat(1)-(1)/(2) hat(j)+4hat(k)`?

A

`(1)/(2)` square unit

B

1 square unit

C

2 square units

D

4 square units

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • What is the area of the rectangle having vertices A, B, C and D with position vectors hat(i) (1)/(2) hat(j) + 4hat(k), hat(i) + (1)/(2) hat(j) + 4hat(k), hat(i) - (1)/(2) hat(j) + 4hat(k) and - hat(i) - (1)/(2) hat(j) +4hat(k) ?

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    C
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    D
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  • Area of a rectangle having vertices : A (-hat(i)+(1)/(2)hat(j)+4hat(k)), " " B(hat(i)+(1)/(2)hat(j)+4hat(k)) , C(hat(i)-(1)/(2)hat(j)+4hat(k)), " " D(-hat(i)-(1)/(2)hat(j)+4hat(k)) is :

    A
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    B
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    C
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  • If [[hat(i)+4hat(j)+6hat(k), 2hat(i)+ahat(j)+3hat(k), hat(i)+2hat(j)-3hat(k)]]=0 then a=

    A
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    B
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    C
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    D
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