Question

Assertion (A): The vectors

`overset->a = 6hat i + 2 hat j - 8 hat k`

`overset->b = 10 hat i - 2 hatj - 6 hat k`

`overset ->c = 4 hat i - 4 hat j + 2 hat k`

Reason (R): Three non-zero vectors of which none of two are collinear forms a triangle if their resultant is zero vector or sum of any two vectors is equal to the third. 

Options

• Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).

• Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of the Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of the Assertion (A).

Explanation:

Assertion:

`|  overset->a  | = sqrt((6)^2 + (2)^2 + (-8)^2) = sqrt104`

`|  overset->b  | = sqrt((10)^2 + (-2)^2 + (-6)^2) = sqrt140`

`|  overset->c  | = sqrt((4)^2 + (-4)^2 + (2)^2) = sqrt36`

`(sqrt140)^2 = (sqrt104)^2 + (sqrt36)^2`

Hence, it forms a right angle triangle.

Reason: Reason is correct but not the explanation of Assertion.