ISC Class 12th Mathematics Chapter 5 - Vectors Important Questions with Answers

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If `veca` is a unit vector perpendicular to `vecb` and `(veca + 2vecb).(3veca - vecb) = -5`, find `|vecb|`.

Question 2.

Find a vector of magnitude 9 units and perpendicular to the vectors.

`veca = 4hati - hatj + hatk` and `vecb = -2hati + hatj - 2hatk`

Question 3.

What are the values of x for which the angle between the vectors? `2x^2hati + 3xhatj + hatk` and `hati - 2hatj + x^2hatk` is obtuse?

Question 4.

Shown below is a cuboid. Find `vec(BA).vec(BC)`

Question 5.

The two vectors `hatj+hatk " and " 3hati-hatj+4hatk` represent the two sides AB and AC, respectively of a ?ABC. Find the length of the median through A

Question 6.

Show that the vectors `veca, vecb` are coplanar if `veca+vecb, vecb+vecc `are coplanar.

Question 7.

Prove by vector method, that the angle subtended on semicircle is a right angle.

Question 8.

If the direction cosines of a line are `(1/c, 1/c, 1/c)` then ______.

0 < c < 1

c = ± 3

c > 2

c > 0

c = `±sqrt(3)`

Question 9.

If `veca and vecb` are two vectors such that `|veca+vecb|=|veca|,` then prove that vector `2veca+vecb` is perpendicular to vector `vecb`

Question 10.

Write the number of vectors of unit length perpendicular to both the vectors `veca=2hati+hatj+2hatk and vecb=hatj+hatk`

Question 1.

Find `lambda` if the scalar projection of `vec a = lambda hat i + hat j + 4 hat k` on `vec b = 2hati + 6hatj + 3hatk` is 4 units

Question 2.

If A, B, C are three non- collinear points with position vectors `vec a, vec b, vec c`, respectively, then show that the length of the perpendicular from Con AB is `|(vec a xx vec b)+(vec b xx vec c) + (vec b xx vec a)|/|(vec b - vec a)|`

Question 3.

Show that the four points A, B, C and D with position vectors `4hati + 5hatj + hatk`, `-hatj-hatk`, `3hati + 9hatj + 4hatk` and `4(-hati + hatj + hatk)` respectively are coplanar