Advertisements
Advertisements
Question
Select the correct option from the given alternatives:
The line joining the points (2, 1, 8) and (a, b, c) is parallel to the line whose direction ratios are 6, 2, 3. The value of a, b, c are
Options
4, 3, - 5
1, 2, `(- 13)/2`
10, 5, -2
3, 5, 11
Solution
4, 3, - 5
APPEARS IN
RELATED QUESTIONS
If `bar"AB" = 2hat"i" - 4hat"j" + 7hat"k"` and initial point A(1, 5, 0). Find the terminal point B.
Show that the following points are collinear:
A = (3, 2, –4), B = (9, 8, –10), C = (–2, –3, 1)
If the vectors `2hati - qhatj + 3hatk` and `4hati - 5hatj + 6hatk` are collinear, find q.
Are the four points A(1, −1, 1), B(−1, 1, 1), C(1, 1, 1) and D(2, −3, 4) coplanar? Justify your answer.
Show that the following points are collinear:
P = (4, 5, 2), Q = (3, 2, 4), R = (5, 8, 0).
Select the correct option from the given alternatives:
If `|bar"a"| = 2, |bar"b"| = 3, |bar"c"| = 4` then `[bar"a" + bar"b" bar"b" + bar"c" bar"c" - bar"a"]` is equal to
If α, β, γ are direction angles of a line and α = 60°, β = 45°, then γ = ______.
Select the correct option from the given alternatives:
The distance of the point (3, 4, 5) from the Y-axis is ______
Select the correct option from the given alternatives:
If θ be the angle between any two vectors `bar"a" "and" bar"b"` then `|bar"a" . bar"b"| = |bar"a" xx bar"b"|`, when θ is equal to
ABCD is a trapezium with AB parallel to DC and DC = 3AB. M is the midpoint of DC. `bar"AB" = bar"p", bar"BC" = bar"q"`.
Find in terms of `bar"p" and bar"q"`:
(i) `bar"AM"` (ii) `bar"BD"` (iii) `bar "MB"` (iv) `bar"DA"`
If Q is the foot of the perpendicular from P(2, 4, 3) on the line joining the point A(1, 2, 4) and B(3, 4, 5), find coordinates of Q
If A(3, 2, -1), B(-2, 2, -3), C(3, 5, -2), D(-2, 5, -4) then find its area.
Let A, B, C, D be any four points in space. Prove that `|bar"AB" xx bar"CD" + bar"BC" xx bar"AD" + bar"CA" + bar"BD"|` = 4 (area of triangle ABC).
Let hat"a", hat"b", hat"c" be unit vectors such that hat"a".hat"b" = hat"a".hat"c" = 0 and 6 the angle between hat"b" and hat"c" is pi/6. Prove that hat"a" = +- 2(hat"b" xx hat"c").
Find the value of ‘a’ so that the volume of parallelopiped formed by hat"i" + "a"hat"j" + hat"k", hat"j" + "a"hat"k" and "a"hat"i" + hat"k" becomes minimum.
If four points `"A"(bar"a"), "B"(bar"b"), "C"(bar"c") and "D"(bar"d")` are coplanar, then show that `[(bar"a", bar"b", bar"c")] + [(bar"b", bar"c", bar"d")] + [(bar"c", bar"a", bar"d")] = [(bar"a", bar"b", bar"c")]`.
If in a tetrahedron, edges in each of the two pairs of opposite edges are perpendicular, then show that the edges in the third pair is also perpendicular.
If |a̅| = 3, |b̅| =4, then the value of λ for which a̅ + λ b̅ is perpendicular to a̅ − λ b̅ is ______
The values of c that satisfy `|"c" bar("u")|` = 3, `bar("u") = hat"i" + 2hat"j" + 3hat"k"` is ______
The vector equation `overliner = hati - 2hatj - hatk + t(6hatj - hatk),` represents a line passing through points ______
If `overlinea = hati - 2hatj + 3hatk, overlineb = 2hati + 3hatj - 4hatk` and `overlinec = 4hati + 13hatj - 18hatk` and `overlinec = poverlinea + qoverlineb` then p + q is equal to ______
Find the values of c which satisfy `|"c"overline"u"|` = 3 where `overline"u" = hat"i" + 2hat"j" + 3hat"k"`.
Check whether the vectors `2hati + 2hatj + 3hatk, -3hati+ 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.
