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

If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are non-coplanar vectors, prove that the points having the following position vectors are collinear: \[\vec{a,} \vec{b,} 3 \vec{a} - 2 \vec{b}\]

If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are non-coplanar vectors, prove that the points having the following position vectors are collinear: \[\vec{a} + \vec{b} + \vec{c} , 4 \vec{a} + 3 \vec{b} , 10 \vec{a} + 7 \vec{b} - 2 \vec{c}\]

Using vector method, prove that the following points are collinear:
A (6, −7, −1), B (2, −3, 1) and C (4, −5, 0)

Using vector method, prove that the following points are collinear:
A (2, −1, 3), B (4, 3, 1) and C (3, 1, 2)

Using vector method, prove that the following points are collinear:
A (1, 2, 7), B (2, 6, 3) and C (3, 10, −1)

Using vector method, prove that the following points are collinear:
A (−3, −2, −5), B (1, 2, 3) and C (3, 4, 7)

Find the angle between the given planes. \[\vec{r} \cdot \left( 2 \hat{i} - 3 \hat{j} + 4 \hat{k} \right) = 1 \text{ and } \vec{r} \cdot \left( - \hat{i}  + \hat{j}  \right) = 4\]

Find the angle between the given planes. \[\vec{r} \cdot \left( 2 \hat{i} - \hat{j}  + 2 \hat{k}  \right) = 6 \text{ and } \vec{r} \cdot \left( 3 \hat{i}  + 6 \hat{j}  - 2 \hat{k}  \right) = 9\]