Recent questions and answers in Vector Algebra

Find the volume of the tetrahedron formed by the four planes $x+y=0,y+z=0,z+x=0,x+y=1$

answered Jul 9, 2019 by meena.clay6

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Find the scalar components and magnitude of the vector joining the points $P (x_1, y_1, z_1)$ and $Q (x_2, y_2, z_2)$ .

answered Dec 6, 2017 by priyanka.c

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If the points $(1,1,p)$ and $(-3,0,1)$ are at equidistant from the plane $\overrightarrow {r} . (3 \hat {i} +4 \hat {j} -12 \hat {k}) + 13 = 0,$ then find the value of p.

answered Dec 28, 2016 by priyanka.c

1 answer

If $\theta$ is the angle between any two vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ , then $|\overrightarrow {a} . \overrightarrow {b} | = |\overrightarrow {a} \times \overrightarrow {b}|$ , then what is the value of $\theta$

answered Dec 20, 2016 by priyanka.c

1 answer

Find the area of the triangle formed where vertices are A (3, -1, 2), B (1, -1, -3) and C (4, -3, 1).

answered Dec 10, 2016 by priyanka.c

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If $\theta$ be the angle between two unit vectors. Evaluate $\sin \frac{\theta}{2}$

answered Nov 30, 2016 by priyanka.c

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If A, B, C are position vectors (2, 0, 0), (0, 1, 0) and (0, 0, 2) show that $\triangle ABC$ is isosceles .

answered Nov 23, 2016 by priyanka.c

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If $|\overrightarrow{a}| = 11, |\overrightarrow {b} | = 23 and |\overrightarrow {a} - \overrightarrow {b} |= 30$

answered Nov 22, 2016 by priyanka.c

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Are the vectors $(\hat {i} + \hat{j} + \hat{k}), (2\hat{i} +3\hat{j} -\hat{k})$ and $(-\hat{i} -2\hat{j} +2 \hat{k})$ are linearly dependent ?

answered Nov 21, 2016 by priyanka.c

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Find the point at which the target to the curve $y = \sqrt{4x-3} - 1$ has its slope $\frac{2}{3}$

answered Nov 21, 2016 by priyanka.c

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Find the shortest distance between the line $l_ 1$ and $l_2$ given by: $\overrightarrow {r} = \hat{i} +2\hat{j} -4\hat{k} + \lambda (2 \hat{i} + 3 \hat {j} + 6 \hat {k}) and \overrightarrow {r }= 3\hat{i} + 3\hat{j} -5\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k})$

answered Nov 20, 2016 by priyanka.c

1 answer

Find the vector and Cartesian equation of the line through the point (5, 2, -4) and which is parallel to the vector $3 \hat{i} +2 \hat{j} -8 \hat{k}$

answered Nov 19, 2016 by priyanka.c

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A line passes through (2, -1, 3) and is perpendicular to the line $\overrightarrow {r} = ( {\hat{i} + \hat {j} - \hat{k}}) + \lambda (2\hat{i} - 2\hat{j} +\hat{k})$ and $\overrightarrow {r} = (2\hat{i} - \hat{j} -3\hat {k}) +\mu (\hat{i} + 2 \hat{j} +2\hat{k})$ . Obtain its equation.

answered Nov 18, 2016 by priyanka.c

1 answer

If $\overrightarrow {a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\overrightarrow {b} = 2\hat{i} + 4\hat{j} - 5\hat{k}$ represents two adjacent sides of a parallelogram, find unit vectors parallel to the diagonals of the parallelogram.

answered Nov 18, 2016 by priyanka.c

1 answer

If the points $A(-1, 3, 2),\; B(-4, 2, -2)$ and $C (5, 5, \lambda)$ are collinear, find the value of $\lambda$

answered Nov 17, 2016 by priyanka.c

1 answer

Write the value of the following: $\hat i \times (\hat j + \hat k)+$ $\hat j \times (\hat k + \hat i)+$ $\hat k \times (\hat i + \hat j)$

answered Mar 21, 2014 by balaji

1 answer

A tow truck drags a stationary car along the road. The chain makes an angle of 30 degrees with the road and the tension in the chain is 1500 N. How much work is done (in Joules) by the truck in pulling the car 1 km (approximate answer, rounded off)?

answered Feb 11, 2014 by balaji.thirumalai

1 answer

Find $|\overrightarrow x|$ , if for a unit vector $\overrightarrow a,\:(\overrightarrow x-\overrightarrow a).(\overrightarrow x+\overrightarrow a)=15$

answered Feb 3, 2014 by rvidyagovindarajan_1

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If the sum of two unit vector is a unit vector, then what is the angle between them?

answered Feb 3, 2014 by rvidyagovindarajan_1

1 answer

What is the angle between following planes $2x-3y+4z=1$ and $-x+y=4$ ?

answered Jan 30, 2014 by balaji

1 answer

What is the area of the parallelogram having diagonals $3\bar{i}+\bar{j}-2\bar{k}\;and\;\bar{i}-3\bar{j}+4\bar{k}$ ?

asked Jan 30, 2014 by balaji

1 answer

If $\theta$ is the angle between any two vectors $\overrightarrow{a} and \overrightarrow{b} ,$ then $|\overrightarrow{a}.\overrightarrow{b} | = | \overrightarrow{a} \times \overrightarrow{b} |$ when $\theta$ is equal to

answered Dec 20, 2013 by meena.p

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True-or-False: Position vector of a point P is a vector whose initial point is origin.

answered Jun 3, 2013 by meena.p

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The vector $\overrightarrow{a}+\overrightarrow{b}$ bisects the angle between the non-collinear vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ if__________.

answered Jun 3, 2013 by meena.p

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If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three vectors such that $\mid\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\mid=0$ and $\mid\overrightarrow{a}\mid=.2, \mid\overrightarrow{b}\mid=3,\mid\overrightarrow{c}\mid=5$ ,then value of $\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}$ is

answered Jun 3, 2013 by meena.p

1 answer

If $\mid\overrightarrow a\mid=10,\mid\overrightarrow b\mid=2$ and $\overrightarrow a.\overrightarrow b=12$ ,then value of $\mid\overrightarrow a\times\overrightarrow b\mid$ is

answered Jun 3, 2013 by meena.p

1 answer

If $\overrightarrow{a}=\hat i+\hat j+\hat k$ and $\overrightarrow{b}=\hat j-\hat k$ ,find a vector $\overrightarrow{c}$ such that $\overrightarrow{a}\times\overrightarrow{c}=\overrightarrow{b}$ and $\overrightarrow{a}.\overrightarrow{c}=3$ .

answered Jun 3, 2013 by meena.p

1 answer

The position vector of the point which divides the join of points $2\overrightarrow{a}-3\overrightarrow{b}$ and $\overrightarrow{a}+\overrightarrow{b}$ in the ratio 3:1 is

answered May 31, 2013 by meena.p

1 answer