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प्रश्न
If `bar("AB") = 2hat"i" + hat"j" - 3hat"k"`, and A(1, 2 ,−1) is given point then coordinates of B are ______.
विकल्प
(3, 3, −4)
(−3, 3 −2)
(3, 3, 2)
(−3, 3, 4)
उत्तर
If `bar("AB") = 2hat"i" + hat"j" - 3hat"k"`, and A(1, 2 ,−1) is given point then coordinates of B are (3, 3, −4).
Explanation:
Given:
`bar("AB") = 2hat"i" + hat"j" - 3hat"k"`
A(1, 2 ,−1)
To find:
B(x, y, z)
`vec(AB) = vecB - vecA`
`vecB = vecA + vec(AB)`
`vecA = 1hati + 2hatj - hatk`
`vec(AB) = 2hati + hatj + -3hatk`
Adding `vecA` and `vec(AB)`
`vecB = (1hati + 2hatj - hatk) + (2hati + hatj - 3hatk)`.
∴ `vecB = (1 + 2)hati + (2 + 1)hatj + (-1 -3)hatk`
∴ `vecB = 3hati + 3hatj -4hatk`
∴ The coordinates of B are (3, 3, −4).
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