# Vector Equation for Straight Line

## Trending Questions

**Q.**The value of p so that the vectors (2i-j+k), (i+2j-3k), (3i+pj+5k) are coplanar should be

**Q.**

The nature of straight lines represented by the equation $4{x}^{2}+12xy+9{y}^{2}=0,$ is

Real and coincident

Real and different

Imaginary and different

None of the above

**Q.**

The point of the curve ${y}^{2}=2(x-3)$ at which the normal is parallel to the line $y-2x+1=0$is

$(5,2)$

$\left(-\frac{1}{2},-2\right)$

$(5,-2)$

$\left(\frac{3}{2},2\right)$

**Q.**If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?

**Q.**In a triangle ABC, a point P is chosen on side −−→AB such that AP:PB=1:4 and a point Q is chosen on side −−→BC such that CQ:QB=1:3. Line segment −−→CP and −−→AQ intersect at M. If the ratio MCPC is expressed as a rational number in the lowest term as ab, then b−a equals

**Q.**Given, two vectors A=-4i+4j+2k and B=2i-j-k. The angle made by (A+B) with i+2j-4k is

**Q.**Does a line have both direction ratios and direction cosines??

**Q.**9. Let vector a = i + j and vector b = 2i - k , then point of intersection of the lines ra =ba and rb = ab is _________? r is arbitrary vector and i, j , k be unit orthonormal vectors.

**Q.**The equation z¯z+(2−3i)z+(2+3i)¯z+4=0 represents a circle of radius

- 2 unit
- 3 unit
- 4 unit
- 6 unit

**Q.**

The equation of the line joining the point $(3,5)$ to the point of intersection of the lines $4x+y-1=0$and $7x-3y-35=0$ is equidistant from the points $(0,0)$ and $(8,34)$.

True

False

Nothing can be said

None of these

**Q.**

The straight line passing through the point of intersection of the straight lines$x-3y+1=0$ and $2x+5y-9=0$ and having infinite Slope and at a distance of $2$ units from the origin, has the equation

$x=2$

$3x+y\xe2\u20ac\u201c1=0$

$y=1$

None of these

**Q.**

The line passing through the point of intersection of $x+y=2,x-y=0$and is parallel to $x+2y=5$is

$x+2y=1$

$x+2y=2$

$x+2y=4$

$x+2y=3$

**Q.**

Let $\mathrm{\xce\pm}$ be the distance between the lines $-x+y=2$ and $x-y=2$and $\mathrm{\xce\xb2}$ be the distance between the lines $4x-3y=5$ and $6y-8x=1$, then

$20\sqrt{2}\mathrm{\xce\xb2}=11\mathrm{\xce\pm}$

$20\sqrt{2}\mathrm{\xce\pm}=11\mathrm{\xce\xb2}$

$11\sqrt{2}\mathrm{\xce\xb2}=20\mathrm{\xce\pm}$

None of the above

**Q.**The projection of the line joining the points (3, 4, 5) and (4, 6, 3) on the line joining the points (−1, 2, 4) and (1, 0, 5) is

- 43
- 23
- 13
- 12

**Q.**Find the vector equation of the line which passes through the point (3, 4, 5) and is parallel to the vector 2^i+2^j−3^k.

**Q.**

Prove that the relation R defined on set A of all lines as : R={(L1, L2): L1and L2 are parallel lines} is an equivalence relation

**Q.**

If $x=ay-1=z-2$ and $x=3y-2=bz-2$ lie in the same plane, then the values of $a,b$ are

$a=2,b=3$

$a=1,b=1$

$b=1,a\xe2\u02c6\u02c6R-\left\{0\right\}$

$a=3,b=2$

**Q.**

Show that the three lines with direction cosines

are mutually perpendicular.

**Q.**The vectors 2i+3j, 5i+6j, . , 8i+xj have their initial points at( 1, 1) ..the value of x so that they terminate on one straight line is???

**Q.**

Let *L* be the set of all lines in
XY plane and R be the relation in *L* defined as R = {(*L*_{1},
*L*_{2}): *L*_{1} is parallel
to *L*_{2}}. Show that R is an equivalence relation.
Find the set of all lines related to the line *y* = 2*x* +
4.

**Q.**

Find the vector equation of the line which is parallel to the vector 3ˆi−2ˆj+6ˆk and which passes through the point (1, -2, 3).

**Q.**

**Find the equation of the line passing through the points**$P(5,1)$** and **$Q(1,\xe2\u02c6\u20191)$**.**

**Q.**ntFind The number of values of c such that the straight line 3x+4y=c touches the curve x/2=x+y .n

**Q.**If A has coordinates (−1, 5) and →a is a position vector whose tip is (1, −3). Then the coordinates of the point B such that −−→AB=→a is

- (1, 2)
- (0, 2)
- (0, −2)
- (2, 0)

**Q.**The distance of the point (3, 5) from the line 2x+3y−14=0 measured parallel to the line x−2y=1 is

- 7√5 units
- 7√13 units
- √5 units
- √13 units

**Q.**Find the equation of the plane passing through the point (2, 3, 1), given that the direction ratios of the normal to the plane are proportional to 5, 3, 2.

**Q.**

Vector equation of a straight line passing through a point given by position vector ¯a parallel to ¯b be is given by ¯r=¯a−λ ¯b, where ¯r , where ¯r is r position vector of a general point on the line and λϵIR

True

False

**Q.**54. Suppose that p , q , r be three non coplanar vectors . Let the components of the vector s along p , q , r be 4 , 3, 5 respectively . If the components of s along (-p+q+r ) , (p-q+r ) , (-p-q+r ) are x , y , z respectively , then find 2x+y+z .

**Q.**

Find the equation of the line in vector and in Cartesian form that passes through the point with position vector 2^i−^j+4^k and is in the direction ^i+2^j−^k.

**Q.**The cartesian from of equation a line passing through the point position vector 2^i−^j+2^k and is in the direction of −2^i+^j+^k, is

- x−2−2=y+11=z−21
- x+4−2=y−11=z+21
- x+24=y−1−1=z−12
- None of these