Maths · Scalar and vector products
The vectors and are so placed that the end point of one vector is the starting p
The vectors \( \hat{\boldsymbol{i}}+\boldsymbol{2} \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}}, \boldsymbol{2} \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}} \) and \( \mathbf{3} \hat{\mathbf{i}}+\hat{\boldsymbol{j}}+\mathbf{4} \hat{\boldsymbol{k}} \) are so placed that the end point of one vector is the starting point of the next vector. Then the vectors are :
- A. Not coplanar
- B. Coplanar but cannot form a triangle
- C. coplannar but can form a triangle
- D. coplanar and can form a right angled triangle
Step-by-step solution
The scalar triple product a·(b×c) = 0, so the vectors are coplanar. Moreover, a + b = c, so the three vectors satisfy the triangle condition (one is the sum of the other two). The triangle formed is not right-angled as none of the dot products are zero.
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