Commerce (English Medium) Class 12 - CBSE Question Bank Solutions

Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.

Find the Direction Cosines of the Sides of the triangle Whose Vertices Are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2).

If l₁, m₁, n₁ and l₂, m₂, n₂ are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m₁n₂ − m₂n₁, n₁l₂ − n₂l₁, l₁m₂ ­− l₂m₁.

If the lines `(x-1)/(-3) = (y -2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z -6)/(-5)` are perpendicular, find the value of k.

Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`

Classify the following measures as scalar and vector.

10 kg

Classify the following as scalar and vector quantity.

Time period

In Figure, identify the following vector.

Coinitial

`veca and -veca` are collinear.

Two collinear vectors are always equal in magnitude.

Two vectors having the same magnitude are collinear.

Two collinear vectors having the same magnitude are equal.

Find the direction cosines of the vector `hati + 2hatj + 3hatk`.

Find the direction cosines of the vector joining the points A (1, 2, -3) and B (-1, -2, 1) directed from A to B.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are  `hati + 2hatj - hatk` and `-hati + hatj + hatk`  respectively, externally in the ratio 2:1.

Show that the points A, B and C with position vectors `veca = 3hati - 4hatj - 4hatk`, `vecb = 2hati - hatj + hatk` and `vecc = hati - 3hatj - 5hatk`, respectively form the vertices of a right angled triangle.

Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of the x-axis.