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Question
The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is `vecr = (5hati - 4hatj + 6hatk) + lambda(3hati + 7hatj - 2hatk)`.
Options
True
False
Solution
This statement is True.
Explanation:
We have given line as `(x - 5)/3 = (y + 4)/7 = (z - 6)/2`
By comparing with equation
`(x - x_1)/a = (y - y_1)/b = (z - z_1)/c`
We get given line passes through the point (x1 , x2 , x3 )
i.e., (5, - 4, 6) and direction ratios are (a, b, c)
i.e., (3, 7, –2).
Now, we can write vector equation of the line as `vecr = (5hati - 4hatj + 6hatk) + lambda(3hati + 7hatj - 2hatk)`
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