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प्रश्न
The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is `vecr = (5hati - 4hatj + 6hatk) + lambda(3hati + 7hatj - 2hatk)`.
विकल्प
True
False
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उत्तर
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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संबंधित प्रश्न
The x-axis and y-axis taken together determine a plane known as_______.
Name the octants in which the following points lie:
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(–5, –4, 7)
Name the octants in which the following points lie:
(–7, 2 – 5)
Find the image of:
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Find the image of:
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The coordinates of a point are (3, –2, 5). Write down the coordinates of seven points such that the absolute values of their coordinates are the same as those of the coordinates of the given point.
If A(–2, 2, 3) and B(13, –3, 13) are two points.
Find the locus of a point P which moves in such a way the 3PA = 2PB.
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Find the foot of perpendicular from the point (2,3,–8) to the line `(4 - x)/2 = y/6 = (1 - z)/3`. Also, find the perpendicular distance from the given point to the line.
Find the equation of the plane through the points (2, 1, –1) and (–1, 3, 4), and perpendicular to the plane x – 2y + 4z = 10.
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The angle between the line `vecr = (5hati - hatj - 4hatk) + lambda(2hati - hatj + hatk)` and the plane `vec.(3hati - 4hatj - hatk)` + 5 = 0 is `sin^-1(5/(2sqrt(91)))`.
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If the foot of perpendicular drawn from the origin to a plane is (5, – 3, – 2), then the equation of plane is `vecr.(5hati - 3hatj - 2hatk)` = 38.
